I say "by accident" and "on purpose." My knee jerk reaction is that the phrasing suggests that accidents simply happen, not having been deliberately caused, while deliberate intent is required to make something purposeful occur. But, I'm not at all certain, as I think about it, that this interpretation has anything at all to do with the pronouns involved, but is, instead, a result of mere long-term association.

I think I've tried a loquat, but I can't be sure. We often try interesting fruit, both fresh and canned, from international markets, and we don't always know the English name for what we try.