I've got a '68, and everything was apart when I bought it. From what I can tell, the trim piece you mention does clip onto the bracket that the headliner is glued to. (If it's like a '68).
Appears to me from the clips on mine that you probably need to push up on it and then it pops off. Again, if the '67 is like the '68 and I'm not making a false assumption.