Seriously, this is the very definition of a shallow dismissal.
Absolutely. In orchestral band back in my high school days, between songs I would ask my friend on the tuba to give me a note for reference so I could tune the timpani. If you are in a band you should be able to manage to take a one second note and hold that by humming or something and tune up. I can't even read real music (I was a "percussionist" ie incompetent except at rhythms) and even I could do that. Better trained musicians than I could expand from there to the other notes you need.
You just need a single reference pitch. You can literally just play a sine wave into your headphones for a second on stage, or have your audio engineering guy feed you one. Or you have one of those dirt cheap tuners that clips to the fretboard to get you started.
The lead singer is engaging in stage banter partially to give you the time and space to do this. If your ensemble includes a pianist or a synth, you just have them slap a note for a reference.
I haven't touched a tuner in about half a decade.
I can believe this is possible. But I don't think this is a reasonable thing as a baseline expectation for a player with 6 weeks of experience, which was the original comment in this thread.
I don't know the details, but I imagine you're feeling beats transmitted through the neck or something. But if that is the case (an assumption) it still requires you to have at least one known-good string, unless you're playing solo.
So, for these circumstances, and others, a pedal-based or clip-on headstock tuner seem like they still have plenty of practical application.
i'm also the one at rehearsal literally throwing TU-3s at my bandmates who don't have tuners on their boards for some reason. you have to have a tuner if you play with others. no question.