Yes, the screws should come with your case, not the motherboard.
SeVeRaNCE, if your friend had problems with using metal screws, the head of the screw must have been larger than the small circular metal ring around each screw hole on the mb, and maybe was interfering with the proper electrical functioning (i.e. the signal was drawn to the conductive screw instead of following the correct electrical path, I assume this is a short, but electricity is not my area) of the board.
Sometimes (I noticed this on Asus boards), there may be an additional outer ring (just an outline, not metal) outside of the inner metal ring, I've assumed, on one occasion, that this is a safety or dead zone, in case the screw is larger than the metal ring. But, this is just a guess.
I can tell you that I built a system a year ago (Asus p3v4x) where the screws were just slightly bigger than the metal rings in the corresponding screw holes on the mb. The screws came with an Antec KS-282 case. I was a little bit perplexed at first, but the metal ring around the screw holes were so small on the Asus board, it just seemed illogical that Asus would have conceived that system builders would never have a problem with screw sizes. Thus, in this case, I believed that I wouldn't have a problem with the screws slightly exceeding the metal ring area on the mb, and the system has been running great since I turned it on for the first time. However, in general, screws should be contained in this metal ring area, and I've noticed other mb makers have large enough rings that this shouldn't be a problem.
If you look at AMD's site, they have a guide for building your own PC (actually Athlon, but relevant nonetheless) in which they suggest that it's important to use screws that do not rest beyond this metal ring, so I would suggest it's important to do so. Finally, I don't think it's a good idea to use all plastic screws, as I believe metal screws play some role in grounding the motherboard (someone correct me if I'm wrong). I hope this helped.