You wouldn't be allowed to stow one of those under the seat with the long dimension fore-and-aft because it would obstruct adjacent passengers' access, so the only permitted way would be cross-wise.
I've always stowed mine end on (when I've had to becuase the bins are full) and never had a problem (except you can't strech your legs out in front of you). The width and height is a perfect fit and the end is flush with the back of the seat. You can't do cross wise anyway becuase there are rails between each seat. We'll have to agree to differ. Anyway this is all getting away from the original question of what cabin crew put in the bags for a flight with no overnight stop.