I think you got it with the Radar Environment requirement.
TRSA's are optional for civilian aircraft, but military aircraft are required to participate in radar control whenever available, so as to prevent mishaps and midairs.
The reason that the gouge probably says TRSA's are to be treated as "Psuedo Charlies" is because under the old airspace system they were Charlie airspace (or atleast, they were the same airspace as what all the Charlie used to be). But under the new FAA system, they did not have enough traffic to become Class C. But, the field the TRSA works for is simply too busy to be only a D airport... it's kind of an inbetween and a holdover from the old system.
Also, the old radar system for controlling aircraft was still in place there... so why not use it? Plus, it can handle the approaches and assist the tower at which it is based, and it technically doesn't require two way comms to enter the airspace. To Note: Although it is a holdover from the old ways, the FAA can still commission a new TRSA if it wants to (For example the Fairbanks TRSA in Alaska was commissioned in 2000)
EDIT:: Sorry, you asked for sources... Well, you named the source where it says Navy are required to operate under Radar Control if available... and as to the history of TRSA's and how they got linked as Charlie airspace, here's one of my links that discuss TRSA's history
http://flighttraining.aopa.org/student_pilot/solo/pdfs/SA02_Airspace_for_Everyone.pdf (look at the note below Fig. 6 on page 6)
Atleast, that's the info this stud learned when he was getting his Instrument Rating.