I know they're not getting drunk off a sip, and didn't say that the sip was the free drink.
They'd do this to young single guys, the type who looked naive, and flirtily take a sip from the guy's drink, making it clear that they wanted a drink of their own. The guy, usually being drunk and stupid, would fall for it and buy them drinks for as long as they kept flirting. At the end of the night, the girls would drop the act and just walk away.
Obviously, nobody owes anyone else anything, and this clearly isn't what OP was doing but if you've been burned by someone taking advantage in the past, you're more likely to think that's what's happening again.