Not true.

There is no implication that Death Metal singers learned their vocal methods from bats, only that they use the same kind of vocal technique.

The statement is that Death Metal vocalists learned to do the same thing bats do naturally, without influence from bats to learn. Not that one directly influenced the other.

That is a big reason why the order is irrelevant.

This is not a statement of cause and effect that links the two ideas as one leading to the other to begin with. It's a comparison of like to like.

It's "A" is the same as "B" and the order of "A" and "B" is irrelevant in that kind of statement.

It is not "A" caused "B" in which case order does matter.

The statement "I poured gravy on my mashed potatoes and it eroded a canyon into them, so it is like the Grand Canyon." does not imply that my mashed potatoes existed before the Grand Canyon did.

This is the exact same situation.

What you're suggesting is like saying that if I say that "Bats and Birds both use wings to fly", it suggests that Bats copied their wings from Birds, and that bats existed before birds did.