The military prohibition has nothing to do with being puritanical, it is a recognition that the vast majority of sex workers are coerced, illegally trafficked, and/or imprisoned and we ought not support that. Reasonable I'd think.
Not the real issue with the Treasury guys. So you're protecting world target #1 but you're going to consort with questionable levels of society and possibly compromise who knows what about your team and schedules. Good one. Makes me think we ought to have security cleared single girls to travel with them so we know what they are into.
Also, another vote for this is probably standard routine. I've traveled with the military, we are pretty mild, confined mostly to wrecking rental cars, strip clubs and lots of beer. But it's a culture. You're traveling as a group, already overpaid by local standards, getting per diem on top of it, and bored with time on your hands. Having known people from the Blue Angels I'm shocked they only crash a plane every couple years. Quality maintenance on those jets is probably not nearly as important as who gets the best rental car in each town. Party, fly, repeat.