@pleonasm - I agree that there are men (and women) who are too cavalier with sex and should be more responsible, I also think ultimately it comes down to each of us to be responsible for our own bodies. And that includes not just taking the word of a sex partner that they are clean because they've never had symptoms.
In fact that would be a huge red flag for me, because anyone who knows anything about STDs knows that a lot of things don't have symptoms in some people, but can have them in others. And other diseases don't have symptoms at all for anyone until you get really sick (HIV is a big one here).
I always insist on a full STD screening for both of us if we're going to start going without the condoms and I only go that far if we've been exclusive for at least a year. A trichomonas infection isn't even one of the bigger risks if you don't take care of yourself.