I actually had a restaurant's owners *tell* me that if we wanted a cake for the party we were planning there, we had to bring our own since they don't do cake (this is a neighborhood pub with great food but a very limited dessert menu -- usually just one or two daily specials). They even arranged it so I could bring the cake over in advance of party time, although they weren't open yet. We did raid their supply of (disposable) plates and forks, since the co-planner, who was supposed to bring them, had a brain fart and forgot. We sliced and served the cake ourselves. There was no fee.
It's quite possible that this same place would charge a party of strangers a fee for an outside cake on, say, a busy Friday night, but GoH, co-planner and I are regulars, and they were thrilled to host this party for their good friend GoH and his buds on a Sunday afternoon, when they otherwise wouldn't have 50 or 60 people in there. They made out very well that day!
Bottom line: Slicing or "forkage" (love that!) fees are not universal. Calling ahead to find out whether bringing an outside cake is allowed/incurs a fee is the smart thing to do, but I wouldn't expect a bunch of teenagers inexperienced with this situation to know that.