Can a carried character use theme team PC? Carry says a carried character cannot be given an action (other than free action). PC is not an action.
And, theme team PC says give the character an action token; it does not say the character has taken an action. With all that in mind, it appears to me that a carried character should be able to use theme team PC. Correct?

I believe you are correct sir.

The only time you could not use a theme team PC is if the carrying character was using hypersonic speed because the carried character is not put down until after your movement is done

But, yes, you are correct

1. PC is not an action
2. Assigning an action token is not an action it is an effect that is triggered by something, usually an action being taken but not always