In general, you are correct, but when I "run the numbers" on my planned system, it is surprising how small the extra capacity is. I'll see if I can do a short version:

My '68 F-350 weighs 6,500 unladen, with a 10,000 GVW => 3,500 net.
Tandem-axle trailer, 2,000 unladen, with a 7,000 GVW => 5,000 net.
Just add the two net weights, because they are independent.
This gives 8,500 unladen, with a 17,000 GCVW => 8,500 net.

My '68 F-350 weighs 6,500 unladen, with a 10,000 GVW => 3,500 net.
Fifth-wheel trailer, 3,500 unladen, with a 13,500 GVW => 10,000 net.
Because 3,500 of the trailer weight is on the truck, the truck's net is already included in the trailer's net, so do not count it twice.
This gives 10,000 unladen, with a 20,000 GCVW => 10,000 net.

I have done this calculation a lot of times and would love to have somebody point out an error. The numbers are in part due to choices already made. I am using a single-axle, dual-wheel configuration the same as my F-350 by my choice. I KNOW that if I went to tandem-axle dual-wheels, the story would be much different. Another part of my loss is the very heavy (2,000#) flatbed I have - I am considering making an abreviated fifth-wheel deck.

There are several reasons why I am still going to build the fifth-wheel:
o I already have acquired almost all the parts.
o I want the stability of a fifth-wheel.
o Some loads cannot be divided between the truck & trailer decks.