Well, guess what? Apparently there is nothing wrong with any of my equipment. The little IR device that transfers the Slingbox signal to the Xfinity box was actually blocking the signal from my Xfinity remote.
I started thinking that maybe people who couldn't seem to change channels with the onscreen remote didn't have the IR thingies in the right place. Then I suddenly realized that maybe my IR thingies were blocking my physical remote. And, yes, that is what was happening.
Sorry for wasting your time, but maybe this will help someone else. Thanks.