Do they really understand?

[snailracer]

A bit more cycling-inform bashing:

...you need your centre of gravity to remain over your tires ...

If that was actually true, the bike would not be turning due to basic physics.

...you’re increasing the traction your tires have on the road...you should lean the bike more than you lean your body...

The road would be in contact more on the tyre sidewall than the central tread. I have no idea whether that gives more grip, but it gives less clearance between rim and road so you have less bump compliance.

... Moving back on the seat helps too!

I can't see how that would help the following:

.... weight distributed appropriately across both wheels...

 

[Kookas]

that it's ever sensible to rock the bike from side-to-side enough to notice.

Doesn't out-of-saddle climbing do that?