Plus the damn logo is right across the chest - yeah that is exactly where I want people to look when talking to me.
My husband wears his as yardwork clothes especially the long sleeve ones since they are made of poor material and look crappy after several washings.
At another company the receptionist (a woman) bought extra tight shirts for the women - all 3 of us decided to throw them away - no way in hell were we wearing that. It was degrading. Then we were taunted by everyone why we were not showing company spirit.
If you want to give swag - give something useful like a electrostatic-free strap. That always comes in handy.
For something to display - how about a baseball hat. Sun gave jean jackets and other jackets - all too big - can not wear but at least it was different. I love the PR suggestion - put your benefit statement and then your logo and your URL.