The problem with that demonstration that is glossed over, is that the dots themselves also get bigger, so the relative distances between them stay proportionally the same.

... their rulers, and indeed themselves, along with everything would also increase in size, so everything would appear to be exactly the same.

No; that would be the case if quintessence were the only factor, but at smaller scales other forces dominate. At the scale of planets, solar systems, and galaxies -- and even within galactic clusters -- gravity predominates. That is, things are pulled together "faster" than expansion drives them apart. And at even smaller scales, other forces (electromagnetic, nuclear) predominate even over gravity. In the balloon analogy, there is no other factor besides expansion. That's a weakness of the analogy.