Take on "on accident"

I am far from the authority on grammar but there is one term that I hear often which bothers the hell out of me.  

People who will say that something happened "on accident".  I have always been of the believe that something happens by accident whereas when something happens for a reason it happens on purpose.  At least this is what I was taught in the second grade but I run across the on accident thing all the time. 

You tell me which is right.  

Cathy fell down at a kid's birthday party by accident but to be fair she did drink six glasses of Chardonnay on purpose 

Cathy fell down at a kid's birthday party on accident but to be fair she did drink six glasses of Chardonnay on purpose. 

I don't think it is close 

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