I’d agree. The Air Force were definitely involved in the Shuttle’s design, as detailed in Maciej Ceglowski’s excellent post from around the time of the post-Columbia return to flight, and their demands significantly changed the project (despite the fact that, in the end, the lunar orbit that the Shuttle was pushed to be ready for was never flown).
There’s also the fact that American intelligence (specifically the National Reconnaissance Office) has long been flying spy satellite missions that required complicated airborne recovery of the photographic payloads. (By contrast, the Soviets used a modified Vostok spacecraft with a parachute landing to ground right through their observing history. Generally, their programme did have a knack of being a weird mix of lower-tech (ground landing) but also higher (pressurised camera housing allowing re-use).)
While the advent of improved electronics allowed the subsequent KH-11 to avoid film return issues, I’m sure it was useful for these to be both launched by and serviceable by the Shuttle; indeed, a 1990 Atlantis launch (STS-36) is believed to have placed an upgraded spy satellite into orbit.
None of this is conclusive, but it’d be hard to believe that the NRO (and probably Air Force) weren’t supporting the Shuttle programme behind the scenes, at least until they got their replacements ready. (Note the first flight date.)
Since the presidential coin programme began, the US government has spent an additional $30m to promote them but they still have not taken hold.
“We have tried every major idea that we can come up with, with limited success,” US Mint Director Edmund Moy told a congressional panel last month.