I was intending posting the exact same thread but you beat me to it. I thought I was the only one who gets irritated by this. This is one of those nuggets that you keep reading that seems completely counter intuitive, so several months back I went looking on physics forums to find out the answer. Like eternal says, it is completely untrue. The opposite is true in fact, standing up raises your center of gravity. Now, if you want to get deeper into it apparently a higher center of gravity make it easier to steer at speed, something to do with inverted pendulum (I admit I got lost at this point). The simple way I think of it is standing on the pegs effectively creates a hinge in your combined mass. As the bike moves one way you can move the other (weighting the outside peg) keeping your combined COG over the wheels and therefore upright.
There are many skilled riders out there who know how to ride but I’m not going to believe them when they start talking theoretical physics. Lee Parks is a prime sinner in this (as well as burying his useful information in layers of obscure quotes and zen existentialism). I’m thinking the number of highly skilled riders out there who have a degree in mechanical physics are few and far between.