Is Treantmonk right or wrong about Mounted Combat?

[Valmark]

It gives one sentence clearly indicating it shouldn't act on your turn (the one about changing initiative to match yours) and one that can possibly be read to indicate it should, if and only if you ignore the first sentence.

If it acts on your turn, it doesn't have its own initiative count to change to match yours.

Except that it does have it's own initiative count normally- it's not like it acts with you if you don't mount it. It still needs an initiative if you dismount.