Yes, there is some truth to it. Many older systems communicate with the central station over an ordinary telephone line. More modern systems will use either a cellular communications link or VOIP.

But, the real truth here is that most criminals are pretty unsophisticated and won't even bother cutting phone lines or other cables. Most break-ins also happen through the front door, so, although it sounds great (and it is actually pretty great) to have contact sensors on every window and blanket the whole place with motion detectors, it's not really necessary. If anything, you only really need sensors on the first floor, because in spite of how the movies sometimes depict these sophisticated, cat burgler types, it's mostly just thugs who bash in or take a crowbar to your front door. That's also why advertising exactly what company your security system is from isn't a big deal: they don't care. They see "security system" and just move on to the next house.