Thanks for posting in the Answers Forum! That's a great question!
When using the Slingbox it does take over the stream from your set-top box. Therefore, if someone is watching something at home, whatever channel you are on when connected to the Slingbox will appear on the home TV. As well as if the change the station, it will also switch the that station on whatever device you're connected to the Slingbox from.
There is a way to avoid this with the Slingbox PRO-HD. All you need to do is connect a splitter to the coaxial cable that goes to your cable box. Then run one coaxial cable from the splitter to the IN on the Slingbox and another cable from the splitter to the IN on your cable box. This will give your cable box and Slingbox a seperate cable signal.
The only downside of doing this is that you will only get channels 0-99, rather than your digital cable.
Hope this answers your question!
The Sling Moderation Team
This isn't correct with regards to DirecTV receivers and probably most satellite television. The support article What broadcast and video standards do the Slingbox PRO-HD and SOLO support? states the coaxial input on the PRO-HD supports ATSC (over-the-air broadcast television) and Clear QAM (unencrypted digital cable) input. The satellite signal coming from the DirecTV dish over the coaxial cable isn't either of these.
The DirecTV receiver can only decode one channel at a time. The output to the television and the Slingbox will be the same--the "home" user and the Slingbox user should both be able to watch TV, but it will be the exact same program on both.