When I'm going all out, my watch says I hit 180 bpm which is pretty darn close to my (220-32=188) max rate.
Also cardiac output is more correctly a function of stroke volume, how much blood is pumped for each stroke. Therefore very well trained athletes actually have a lower max hr.
Also cardiovascular drift can increase your max HR, this happens when it's very hot or you have lost a lot of water due to sweating, this causes stroke volume to decrease and heart rate to increase while you still at the same physical output. You hear ppl saying my heart rate was so high and i didn't feel like i was working that hard, it's usually due to cardiovascular drift.
But you are correct to point out that your parent is very far off the mark. Max HR is not a useful predictor of performance, and you can not calculate it with a formula. What you want is a test to exhaustion to determine it, but these are highly dubious due to the psychological aspect, and at the end of it you might have a correct value for max HR, only to realize that it is pretty useless for any prediction purpose.
Case in point, Chris Froome, winner of the Tour de France in 2015, has a max HR of around 170, yet he can sustain 450W for a hour. Meanwhile plenty of people with a max HR of 200 and beyond can't climb stairs without heavy breathing.