Is it correct to say "on accident" instead of "by accident"?

There is a great chasm on these phrases in the US. The great divide seems to be currently centered at the age of 40. The younger generation has began shifting to "on accident" for unknown reasons. What is your view?

"On accident" (meaning "accidentally") does seem to be an unusual usage that frequently appears in opposition to the much more idiomatic "on purpose" (meaning "purposefully"). These are the kinds of idioms commonly used by e.g. children in explaining why something has gone wrong:

—"You broke my toy on purpose!"
—"No, it was on accident!".

A quick survey of the 34 incidences of "on accident" in the Corpus of Contemporary American English show about half have the sense discussed here, and "on accident" does occur in opposition to "on purpose":

HAAS: That happens in so many cases where you're got misinformation that's either leaked on accident or on purpose.
— from "Gunman Kills 32, Wounds 28 at Virginia Tech" on On the Record w/ Greta Van Susteren on Fox News, 2007

JACOBUS: Big difference when it's on purpose and when it's on accident.
— from "Dean, Democrats and Iowa's Deadline", on CNN, 2003

Other examples are from fiction:

"Dad better not see this or you'll get it. I'll tell him we were play fighting, and I slugged you on accident."
— Evan Shopper, "If I have to hit one of you, I'll hit you both" in The Massachusetts Review, 2003

She was thirteen years old, called herself a "gangsta ho" even though all her friends were white, and had already dropped out of school. "On accident," she said - she'd broken her collarbone the year before horsing around on her cousin's dirt bike and missed so much school that she simply never bothered returning.
— Emily Shelton, "From MEMPHIS (Short story)." in Chicago Review, 2003

"By accident", in contrast, has 1419 results, making it more than 100 times more common, and occurring not just in spoken and informal written English, but also in formal edited writing in academic journals, magazines, and newspapers.

"On accident" sounds strange to me. "By accident" sounds better, but I can't understand how it could be much different from "On purpose", albeit very strange to say "By purpose".