I think the girl should have the cover. As others have mentioned, guys with a SO can't afford to be caught carrying one. I had a provider freak out on me one time and claim that since I didn't have any covers on me that I must assume she was going to do BBFS! (not posting the girl's name, but look at the Dallas alerts from a few months ago if you want to know)
She ended up doing a cash and dash because I made her "uncomfortable". After she left I found 10 rubbers in the nightstand drawer.....lol. I can laugh now, but let me tell you I was pretty pissed about it then when I was naked on the bed and she grabs a quick pair of shorts and tube top and jets out the door with my money.