regardless of what were the previous two rolls -- let's call them "X" and "Y" -- if the next roll comes up 20, we are witnessing a sequence "X, Y, 20", which has a probability 0.0125%. That's true even when "X" and "Y" are different than 20.

Yes, all sequences X,Y,Z are equally (im)probable if the d20 is a fair one. But some sequences -- in particular those with X=Y=Z, and in more-particular those with X=Y=Z=1 or X=Y=Z=20, are more likely if the die is unfair because they're relatively easy and/or relatively useful/amusing for a die-fixer to induce.

As you consider longer and longer sequences 20,20,20,... their probability conditional on a fair d20 goes down rapidly, whereas their probability conditional on a dishonest d20 goes down much less rapidly because there's some nonzero chance that someone's made a d20 that almost always rolls 20s.