If you have digital cable and only one cable box then the TV and Slingbox will have the same channel showing.  If the sling changes the channel then the person watching at home will have the channel changed since you are controling that cable box. But you could split the line and go into the sling box that have tuners like the Slingbox Pro to control the non-digital channels(Analog/Basic).  Or you could  get another Digital box from your provider and use that with the Slingbox.  Providers like Comcast charge extra for that digital box per month.  Anywhere from $5.00-$10.00 but it may be worth it.  Spliting the signal will give you only analog channels without a box and your digital box will uneffected. 

Hope that helps....    Happy slinging.... 

It all depends on if you are using a cable box or not.  The Slingbox itself does not give you this limitation.  It's the cable and satellite boxes.

 Forget about the Slingbox for a second.  If you connect a coaxial cable to the out jack of the cable or satellite box (whether it's digital or analog) and then connect that to 2 way splitter and then to 2 TVs, those TVs will be watching the same channel.  It's not that the Slingbox won't allow it, it's the digital cable boxes.

 In the Slingbox Tuner,  the remote viewer and local viewer do not conflict at all.  The Tuner basically has a built in splitter, and analog cable can be shared without cable boxes unless you want the premium channels.

Think of the Slingbox as a TV because that's kind of what it is.  Think of it as if I hook these two TVs to the same jack, do both TVs have to watch the same channel, whether that would be the same TVs (slingbox and actual TV) to a wall jack or a jack on the back of a cable/satellite box.