I am not a crew member, nor have I ever been, but wanted to throw a few words in here. When I was 18 (8 years ago), single, and a passenger on Princess, I was given sooooo much attention by the crew-- welcome with one person, not at all with others--- that it is hard to believe anyone would think it doesn't happen!
I was given free drinks in a room off the dining area (for crew only), champagne was left in my room for free, a pin that crew members wear was made with my name on it, I went up to a basketball court with a dining staff worker, 2 dining staff members came to visit my friend and I in our rooms, etc. The list truly does go on. The physical contact stopped at a kiss with one person, but only because I literally pushed the guys away. My friend established a rather quasi-relationship both on board and off board with 1 guy from the dining staff.
My point... it DOES happen, and apparently quite often, as I've also witnessed this with someone else aboard Royal Caribbean. I don't consider it a huge problem, but I also wasn't aware of how detrimental it is supposed to be for staff members.