your thinking is not invalid. You will still absorb damage and not die. WoW is set up in such a way that you could probably stack strength and still not die.
The reason why Mastery is a huge factor is because the damage mitigation smooths out overall damage taken to a lower number. You will take more damage overall, but each hit received will be normalized. This makes healer's life easier.
Stacking stamina does nothing for damage taken, just gives healers more play room. On a fight where you can live through every large hitting ability with no heals, stamina becomes useless.
Becoming "unhittable" will only do what I mentioned above, smooth out your damage to make damage more predictable and thus easier to heal.
By being a "stamina stacker" you are only giving your healers more room to play with in terms of how much time they have to get back to a safe level of hp. If you run with bad healers, stamina may be a better option because their slow reaction times or terrible heal assignments may cause you to die even though you had shield wall and shield block up.
Doing things because the "top 200 guilds do it" is a terrible reason to do anything. You need to figure out what works best for your healers and your raid team. My damage in take was graphed in comparison to the sustainable HPS of my tank healer. We found that on average, she can keep me alive on most fights without running out of mana.
My big question is: Why are you stacking stamina at all?