Ha! I wish I had a real in-depth knowledge. To give an analogy, if award booking was like chess, then I can say I like to play chess and have experience. I'm not Gary Kasparov.
Your conclusion about different availabilities per programme are quite possible. Definitely quite natural for some programmes to hold seats on the host airline for its own members. That said, it doesn't mean it is not available for redemption from another programme, e.g. US. Only way to find out is to call and try, though.
Another good example is the intra-Europe availability on BA. Search on the AA site (which can look for BA flights), and you may get only a few flights a day for some sectors on some days. Search on the BA site and it's open slather for the same days. CX availability is the mystery
par excellence in this regard, both with underreporting and overreporting of availability.