True, for their UI, similar to Samsung's TouchWiz name. For that matter, HTC was able to get just "Touch" for one of their phones.
A difference, I think, is that Apple does not (and probably cannot) go after anyone who simply says their device has multi-touch (lowercase), and HTC cannot go after anyone who says they make a touch phone.
They probably could. Differences in punctuation or capitalization are of little consequence linguistically - the test is whether the general public would likely be confused and believe that Apple provides or otherwise endorses these other devices.
Wouldn't App Store fall into the same usage? So people could still say they had an "app store", just not the "App Store"?? If so, then I would lean a bit more toward's Apple's side.
Nope.