When to write the word “parenthetically”

I understand that if you're speaking a phrase in which you would write parentheses, you can say the word parenthetically. But when should you write the word parenthetically?

I came across this sentence, starting off a paragraph in a scientific article:

Parenthetically, we note that subjects in all experimental conditions were unbiased …

This struck me as odd. If they're speaking parenthetically, shouldn't it be in parentheses? On the one hand, from a descriptive point of view, the usage of the word was not ambiguous – I know exactly what the author is trying to connote by using it. But from a prescriptive point of view, would this be considered proper grammar?

The use of parenthetically is not limited to the literal meaning of appearing between brackets. It can, as in your example, mean simply ‘as an aside’.

Don't confuse the punctuation marks routinely used to convey an idea with the idea itself, even when the punctuation marks have a same or similar name as the idea. It's quite reasonable to say, "Charles QUESTIONED the speaker's statement" without using a question mark (because I do not actually quote the question). "When I asked my children where they wanted to go for vacation, they EXCLAIMED that they wanted to go to Disney World." Etc.

In addition to its prescriptive purpose, parenthetically may also be used in a more abstract sense, by definition:

Set off within or as if within parentheses; qualifying or explanatory

It's worth noting that there is a difference between a parenthesis and parentheses, the former being a rhetoric device and the latter being punctuation. (Parentheses usually - but not always - enclose a parenthetical remark.)

It's a good word to use in speech, when you can't show actual parentheses. In the context you give, it's probably just a stylistic choice, if an ill-advised one. Parenthetically, I note that scientific papers are not always models of perfect grammar and word choice.