Growing up, the audio tone for that signal was etched into my brain over the course of numerous Saturday mornings, when I woke up early enough to hear the tests. This was before cable was normal. Sometimes it felt like the dial-tone-like noise drilled into your ears for a solid 90 seconds.
Example: https://www.youtube.com/watch?v=oOVwgKmzROw
The new sound is even worse (and seemingly longer), and I imagine it's signal (which sounds more like fax machine squelches than an alert noise) has been crafted to prevent incidents like you describe.
Example: https://www.youtube.com/watch?v=Llrkn2ASVNQ
Also, to prevent deliberate piracy, which was something of an urban legend, but with real, known examples, like the Chicago Max Headroom instance:
https://www.youtube.com/watch?v=tWdgAMYjYSs
It's interesting, because I had always thought the noises were intended to capture the interest of viewers, since it sounds like something of an alarm. It never occurred to me that it might be a system-level control signal. Which makes much more sense now, since the tests were called out as tests, and not drills to prompt viewer activity.
It's funny, because after decades and decades of listening to the test drills, on 9/11 I had expected to hear it cutting in, but it was largely absent and unused. The only time I've ever heard it for real, was during weather-related situations like hurricanes.