Did Peter Piper steal a peck of American pickled peppers?

In the children's renowned tongue twister, which was first published in London 1813, we learn

Peter Piper picked a peck of pickled peppers.
A peck of pickled peppers Peter Piper picked.
If Peter Piper picked a peck of pickled peppers,
Where's the peck of pickled peppers Peter Piper picked?

It seems that Peter picked the equivalent of 9 kg of fresh peppers (a peck) that were either destined to be pickled or perhaps he took the pickled delicacy from a vat.

Could it be that Peter stole the pickles? Etymonline says the verb pick took on the sense of “to rob, plunder” which was later watered down to “steal petty things, filch or pilfer from” by the late 14c.

Were capsicum peppers grown in England? Perhaps they were a well-known delicacy imported to England? I searched in Google Books for the recipe of pickled peppers in the 19th century and found very few references, and from what I could tell they were all by American cooks. The earliest reference I could find is from the American The Valley Farmer- Page 405 printed in 1854

EDIT
I found an earlier recipe dated 1850, from a book entitled Practical Cook Book Containing Upwards of One Thousand Receipts… by Mrs Bliss, a Bostonian.

PEPPERS

Pick the peppers late in the season, just before they begin to turn red; soak them ten days in a strong brine of salt and water; then, if they have a good green color, remove them from the brine to clear cold water, in which let them soak twenty four hours; if they have not a good green color, they will get it by a scalding in the brine; drain them, and if you wish them very hot, pack them away whole in cold vinegar; if you wish them very mild remove their seeds–scraping them out through a slit cut in the side of each pepper and pack them in vinegar. They ought to be good pickles in eight weeks.

• If Peter Piper picked a peck of pickled peppers, is there any evidence to suggest that children or readers in the 19th century would have understood Peter was a thief?

• What type of peppers were pickled in 18th and 19th century England? I don't think Capsicum peppers were ever grown there.

It seems that the word "picked" in the tongue twister does relate to pickpocketing/stealing:

There is some debate among historians over whether the French missionary, botanist, and master smuggler Pierre Poivre (literally "Peter Pepper") was in fact the original Peter Piper who, legend has it, picked a peck of pickled peppers. Certainly his name suggests a direct link (piper is Latin for "pepper"), and while pickled peppers do not appear in his biography, he did manage to pickpocket other valuable spices from the epicenter of the Dutch monopoly. Born in 1719, Poivre led a globe-trotting, multidisciplinary life.

(Wonderland: How Play Made the Modern World (2016))

Pierre's surname means "pepper" in French, leading some authors to identify him as the subject of the Peter Piper rhyme.

(Wikipedia)

Here are two examples to suggest that people understood pick to mean "steal" and assume that Peter may have been a thief // Or people using the tongue twister in the context of picking/stealing:

"You know, Mrs. Dyer, I simply couldn't settle what to call this wicked angel." And she looked deprecatingly up into the face of the cook, who, professing detestation of all animals, secretly adored them. "I shall call him Peter Piper, because, you see, he would have picked a peck of pickled pepper if he could possibly have managed it, only he sneezed too much."
"It's taught him a lesson about stealing off kitchen tables, I should hope, miss," Mrs. Dyer responded grimly.

(The Windsor Magazine: An Illustrated Monthly for Men and Women, Volume 46 (1917))

"The first degree of evidence, and that which, though open to error and misconception, is obviously most satisfactory to the mind, is afforded by our own senses" (Taylor on Evidence, edit., 1885, vol. 1. p. 497).
Consequently the fact-finder must be very careful to collect all the things still in existence which may possibly throw any light upon the matter in issue. "If Peter Piper picked a peck of pickled pepper, where is the peck of pickled pepper Peter Piper picked?" The absence of such an article is often a conclusive objection to the prosecution for picking and stealing, where the prisoner has had no opportunity of disposing of the property.

(The Irish Law Times and Solicitors' Journal, Volume 36 (1902))

There's a mention of this tongue twister in a literary essay dated November 14, 1799, but the pepper isn't pickled:

"Peter Piper pick'd a peck of pepper;
If Peter Piper pick'd a peck of pepper;
Where's the peck of pepper Peter Piper pick'd!"

(Literary Leisure; Or, The Recreations of Solomon Saunter, Esq: (1802))

Some possible interpretations:

• The word "picked" could be an allusion to Pierre Poivre's "clandestine smuggling forays (to steal plants and seeds from the Dutch Spice Islands in 1769–1770)".

• The variation involving "pickled" peppers (from 1813) was probably meant to spice up the original tongue twister (from 1799, see above). Or perhaps it was meant to narrow down the type of pepper used in the original tongue twister.

Is there any evidence to suggest that readers understood pick in the rhyme as steal? No.

The best evidence would come from direct treatments of the poem that acknowledge the alternate reading. For instance, if an expanded version of the poem played on pick as stealing, that would show that the interpretation did occur. The Alexandra Daily Gazette (Virginia), April 27, 1812, has this poem, titled "The Feast":

Good Peter Porter pick'd a peck of pepper. His food to season, for his guests were sick; If for six month's he did the same each day, How many pecks of pepper did Peter Porter pick?

The less compact usage adds more context. Peter picks a peck of pepper (a quarter-bushel) each day to season food for his guests. There is no sign that he stole it, or in the hypothetical he'd have a terribly inattentive victim.

If an essay applied the reading of pick as theft to the poem, that might also be convincing. I found something in Sentinel of the Valley (May 23, 1844), where in an entry titled "Levity" the author offers an essay on the poetic and narrative qualities of the rhyme. The essay is tongue-in-cheek, but nonetheless offers a window in how Peter's actions are understood:

No one can retain even a momentary doubt of Peter Piper's diligence, industry, and application, and no one but must regret, that talents so conspicuous were devoted to the occupation of picking pepper, rather than writing commentaries upon Shakespere.

Peter is industrious, not a thief. The essay goes on in this way with considerable bombast, but the author never interprets pick as theft. Even when he mulls over the question of whether Peter Piper picked the pepper (overreading into the word "if"), the question is only whether he picked it or not, not whether he gathered it or whether he stole it.

Other usages of pick(ed) a peck support that, e.g.,

Mrs. Carry of Mabaska county, aged 82 years, walked a mile and a half to the celebration on the Fourth, walked home at the conclusion of the exercise, and then picked a peck of beans, and took them to market before supper! (Sioux City Register, July 22, 1865)

I saw a man and boy just returned from the woods - one had picked a peck of walnuts, and the other had picked a patridge [...] (Litchfield Enquirer, November 7, 1867).

The reading of pick as steal is tempting, especially after the rhyme changes to pickled peppers and the question turns to where the peck is. Perhaps we are trying to find contraband! However, I could find no evidence to show that people read the rhyme or pick a peck that way.