Actually LindaNoll brings up a good point here which might shed some light on the idiom. Alcohol lessens inhibitors in the mind, and thus many people say things when drunk that they might otherwise reserve when sober. I think at least one intended meaning of the phrase is that if you want to get a guy to spill his guts, get him drunk as a skunk. However, be wary of the literal spilling of the guts if he drinks too much.
No, there is no theoretical proof to it. This is just a phrase often used. However, there is truth to the phrase "dead men tell no tales but drunk men do." This has been proven in many obvious settings due to the talkative and care-free nature of drunken characters.