Help solve a family argument.

Skipbo,
Playing with the family on hols, if you're not familiar with the game , it's basically 160 cards numbered 1-12.

You got to get rid of your deck into a community deck in the middle of the table , building stacks of cards numbered 1-12.

After dealing players cards You draw cards from a face down pile of cards which everyone takes from in turn.

NOW, when a pile is complete of 1-12 it gets discarded until there are no more face down cards , shuffled and your new deck is formed.

However, my in laws , once a 1-12 stack is complete they immediately shuffle the 12 cards and put them underneath the face down deck which you draw from.

I told them that it's wrong, because when you get to those face down cards, that you now have pockets of cards , albeit shuffled, ranging from 1-12.
They argued it doesn't matter , because they are shuffled. I couldn't explain it to them in layman terms.
Please help