Is the flying club Part 141? I used Montgomery GI Bill to finish up my training but had no military flying club available in the DFW area. That was all pre-9/11. I used the Quantico MCAS flying club in the early 1980s to build time. Many of the instructors were retired military IPs. Sadly, the Quantico club no longer exists.
I haven't rented a GA airplane in a long time, so I can't tell you if the manager's quote is accurate. Too good to be true? That's up to you to decide.