Thanks for using our answers forum here, that's a great question! However, if someone is accessing the Slingbox remotely it will change the channel on the cable box at home. The Slingbox doesn't create an independent video stream and when using the SlingRemote it is communicating with the cable box just like your physical remote would at home. The only way the remote stream and the viewing at home could be separate would be if you had a dual tuning cable box, or two individual cable boxes (ie: one connected to the Slingbox and the other to the TV). Does that make sense?
Hope this helps!
The Sling Moderation Team