Here's how I look at it: it's not about trusting my girl at all when it's a situation like this.
It's about that guy KNOWING who she's with and still feeling brave. That's disrespect. That's like him saying "I see you, know the situation, and I'm not worried".
Oh, really? You're not?
I'd give him a friendly how's it going at the gym, re-inforce what the situation is in a very cordial matter just so I know beyond a shadow of a doubt that there is no misunderstanding. Then, if it continues...well, I'd invite him to step into my office to have a more serious discussion (my office being the gym parking lot). Then we'd see if his not being worried was warranted, or a mistake.
It's about the respect, not about trust.