First of all, saying he laid off the booze doesn't mean he was drunk in the incident. Could have been high and drunk, just high, whatever. He's not going to come out and make a statement about not doing coke. This just reminds people about his test. Saying he laid off the booze is another way to say "I'm living clean." He's saying he's a tea-totaller.
Second, speaking from experience, alcohol is the number one gateway drug for those who have had substance abuse issues. Anything that lowers inhibitions is going to make you more likely to go back for one more taste.
Jones is on the right path. I personally can't stand the guy (or at least the guy he was) but I'll be damned if he wasn't an amazing fighter.