cable to the TV set and it gives her cable TV. She says that the company does not split the signal, so it all depends on the processing equipment (computer gets Internet data, TV gets TV signal). If that's true, I'm game.

It was not true for Comcast here in Fort Collins for me

the other line on the split wire runs to another splitter that goes to the tv's in the house.(if you only have one then its a direct line from the home run split..

on the line at the drop in the street.

The cable companie may or may not run an audit at some point. And put the trap on.

At least, thats how we do it.

however - "I've heard that the cable company can scan / ping / check the resistance in the line - so if you pay for internet only but they see lots of connections on the line - that may be a clue you don't have just the cable modem hooked up"

I have no idea about the parts in quotes - just something I was told.