A big fan of the Slingbox as an international traveler.
I have problems getting the HD resolution to work consistently on my Windows 8 computers. As you drag across the pointer it stops at the "best" resolution. I suspect it might be that the bandwidth where I'm at is not sufficient but haven't seen any confirmation.
You are correct that bandwidth is likely the primary issue why you may not get full HD quality.
This article expands on some of the main impacts to picture quality: Slingbox.com - Why am I not getting better video quality?