If I watch live TV remotely and change the channel, it will change the channel on the cable box, thus the person at home will be interrupted. Am I thinking clearly?
I want to setup so that I can watch remotely without the person at home being interrupted - since Comcast requires cable boxes to get many of the HD channels - would I need a separate box?
If Comcast broadcasts any unencrypted QAM channels over their service then you could use the internal tuner of the Slingbox Pro-HD. The hybrid analog and digital tuner is compatible with over the air ATSC and clear QAM signals. If the cable service provides a compatible signal for any channels then it will work with the Slingbox.
Would it make more sense to get a Tivo box plus a CableCard; would that solve the issue?
Yes, the best way to not interrupt the local viewers is to tune into a video source which they aren't watching. Getting another box like a Tivo would definately resolve your issue. Although instead of getting a TiVo box, I would recommend looking at the Moxi (http://moxi.com). It has many more features than the Tivo without the subscription fees.