Here's what might be happening, just a guess since I don't have knowledge of internal of U-VERSE other than U-VERSE routers uses QOS:
U-Verse IP-TV traffic is prioritized over other network traffic and uploads (SLINGBOX network traffic) interfere with TCP download traffic because they can interfere with the flow of acknowledgement data needed by TCP protocol.
SLINGBOX traffic might be messing with recorded playback data flow from boxes that uses network (all boxes other than the PVR one) since everything that is not live TV is not prioritized and most probably uses TCP protocol. Normal IPTV traffic might be using UDP whch doesn't need acknowlegement, thus not affected by uploads.
But again, this is a guess and the cause might be something completely different.