Women vary during their periods - some want sex while on the rag, some don’t. Some get crampy from sex during their period, some don’t.
I had a boyfriend that was OK with sex during That Time of the Month - I found more often than not a good round of sex would relieve cramps. But that’s me.
And yeah, we’d put down a towel.
My current wife, and my late wife both liked it as long as they weren’t in the heavy portion of their periods. As far as the cramping, they also both said it relieved some of the cramping. The joke was that I was knocking something loose in there. 
No big deal at all. I am washable.
I think this is the kind of guy your girlfriend was talking about, OP.