Honestly why does that prove anyone wrong? Because some guy's website says so? Somethings on that site are obviously mistakes ("for all intensive purposes"), but the whole "on accident" or "by accident" is totally arbitrary. There really is no reason why one preposition would be preferred and as language evolves it seems different groups of people use different prepositions. Even if one way was the primary usage in the past, I'd hardly say that that makes another one wrong.
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