Info: some animals get iterative attacks, even when polymorphed

It seems that animals who have only one single natural attack get iterative attacks:

While those that get more than one attack don’t:

Notably, the animal companion keeps the iterative attacks even if they’re polymorphed, seemingly even on the off-hand:

While characters and animals without iterative attacks don’t:

This gives certain animals a lot more attacks if polymorphed and makes, for example, a dog polymorphed into a smilodon a lot more powerful than a smilodon (or a smilodon polymorphed into a smilodon).

I have checked this behaviour for horse, smilodon (both don’t get iterative attacks), wolf and boar (who do).