That's not how I read the situation at all. It seems to me that he and his buddies were drunk, pissed in an alley, broke something in the gas station, then tried to buy their way out.
If you look back, Lochte's mother was the first one to tell this story to the press. It's most plausible that he gave her a bullshit story to save face and she screwed him by "standing up for her son" and talking publicly. Rather than coming clean, he then decided to double down on the lie, and here we are.
Facts are still coming out, but from what we know so far it's pretty clear the security guard extorted them, and now the gubmint is extorting them too. If they broke the law by vandalizing the gas station, then charge them with that. instead they're saying pay us as an apology for saying we're corrupt, and we'll make all your legal problems go away.