I haven't yet fitted a headliner to mine (a '50 3100) but was always under the impression it was secured/held at the front by the inner garnish mouldings,I wasn't aware the rubber actually overlapped it?
If it does,that's news to me.
I always thought the biggest issue was the door windlace rubbers which I believe DO overlap.

Someone will chime in soon with a definitive answer,hang tight!

1950 Chevy Advance Design 3100 in Scotland
In the Stovebolt Gallery
More pix on Flickr.
I've definately got this truck thing in my blood ... my DNA sequence has torque settings
"Of all the small nations of this earth,perhaps only the ancient Greeks surpass the Scots in their contribution to mankind" Winston Churchill.