I'm pretty sure that is incorrect. I routinely carry my phone in areas with extreme sensitivity to any electromagnetic emissions. I have to turn my phone off at those times. If my phone were emitting anything, it would be detected and I'd be told.
The "ping" feature is passive. Your phone isn't transmitting while it's off - but it is
still listening. Like an AM/FM radio, it doesn't emit anything while listening - only while transmitting.
It is listening for the command to "ping" its location. If it doesn't hear the signal, it never transmits anything. Since it is extremely unlikely that the government or cell provider routinely "pings" your particular phone randomly, it likely hasn't occurred any time you've been in the RF sensitive-areas, and thus the phone has never "answered" the ping and emitted RF signals.
I know it sounds unbelievable, but I used to work in the wireless division of Nortel Networks (remember them?). But don't take my word for it: https://ssd.eff.org/wire/protect/cell-tracking
Unfortunately, if you want to use your cell phone at all, avoiding the threat of this kind of real-time tracking is nearly impossible. That's because the government can track your cell phone whenever it's on, even if you aren't making a call. The government can even track some cell phones when they are powered down, unless you have also removed the battery. So, once again, there is a security trade-off: the only way to eliminate the risk of location tracking is to leave the cell phone at home, or remove the battery.