Brian,
It is soil related. The (overly) generalized theory of USGA Greens in 1968 (when introduced) was that with the development of irrigation and fertilizer technology, those items could be replaced when lost, making soil compaction the biggest greens maintenance problem. Sand is the only soil type that theoretically won't compact, although in actual practice, it still needs aerification. We'll say it compacts far less than other soil types.
I have only done push up greens when I have a decent sandy soil with less than 5% silt and or clay. I understand they do push ups in Florida and Palm Springs, owing to the pure sand underneath.
You can put any amount of contour you want in a USGA green, providing you do it in the sub grade and gravel layer. The topmix layer should remain very close to 12" depth throughout. Higher and you get dry spots, lower and you get slower drainage, or god forbid, an area where you can't set an 8" deep cup if you really skimp.
Other than the exceptions mentioned above, I doubt any gca types are doing push ups. If we need to save money, we use "California" greens, which eliminate the gravel layer and peat moss ammendments in the top sand layer. Some may make other cost saving USGA modifications, like rototilling in peat moss, using out of spec sand or other methods, but most agree that sand based is the way to go, again, on account of compaction.