If a part from a competing carrier is used, it may leave that carrier in the lurch if it also needs that part. So understandable if a carrier refuses access.
Ah, the navy storekeeper logic. If he has to have a minimum of one item in store, then you can’t have it, even if you are the ONLY potential user in the country.
There is, or at least was, a pool for engines and various other components. Being part of the pool meant you had to contribute components to the pool, and probably cost serious $ as well. As a general rule, pool items were never available to anyone outside of the pool. Consider it being insurance, and attempting to buy that insurance after the event is, of course, not going to fly.
I once refused to accept an MEL out of Dubai. It wasn’t on a whim, I’d done so in the past and it taught me to never accept that particular MEL again. EK had the part we needed, and after waiting some hours for it to be produced, during which I expect a number of people hoped I’d relent, we had it installed and set off. I was told that it was costing $five figures per day, and that EK wanted it back on the next possible flight.
Airlines can have agreements with each other, but I wouldn’t expect it to be too strong where outright competitors are concerned.