Hello.

so is it his PTSD?

No.

or is he (intentionally or not) using it as an excuse?

It likely causes him real anxiety, but it's still an excuse. He's attempting to control your behavior because he's unable to control his own anxiety and irrational fears. He needs to learn to trust others. But instead, he just blames his behavior on PTSD as if that makes him not liable for his own behavior, and then demands that you tiptoe around his psychological issues. Seems a bit unfair, doesn't it?

does this make his behavior understandable and justifiable?

No.

how do I go about talking to him about this and helping him?

This is a job better suited for a therapist.

Shouldnt he trust me by now?

Yes.