Perhaps it's just a case of correlation being confused with causation.

Always a possibility but most of the studies take that into account.

People who overeat most likely have problems with impulse control, which of course can also lead to problems with alcoholism.

Yes and these things are all inter-related. Activation of the reward pathways is also strongly implicated in problems with impulse control.

Impulse control is a fascinating subject, though. I think a lot of how we manage in life has to do with whether or not we control our impulses.

For sure. I wish I had better impulse control! You have given me an idea for future posts - I'll see if I can find an open access review of the literature on impulse control :)