That sounds plausible. Apparently my phone can then distinguish a ‘personal hotspot’ (internet tethering over wi-fi) from a regular wi-fi router. Which is impressive, unless that nature is broadcast along with the SSID.
My experience with cell phone hot spots is they typically have name like "Joe's iPhone" but the symbol is as shown
here. But then I never have "Ask to join networks" turned on to conserve battery life.