Spike damage is the most common cause of deaths in raids. A lot of time this comes from non-physical sources, like a spell that a boss uses. So most gearing techniques for a tank don't mitigate magic attacks (you can't dodge or block magic). Stamina then gives your healers a larger cushion to deal with the spike damage.
Big magic attacks are almost always on a set timer. Proper usage of cooldowns will totally prevent those spikes. Most of the dangerous spikes are caused by failing to avoid several melee attacks in a row, which is why haste/mastery gearing is preferred (because they don't rely on avoidance to reduce damage).
Stamina will give you a larger cushion to deal with spikes, that's true. Stacking stamina at the expense of other stats will also cause you to take more damage, forcing the healers to spend more time and mana healing you for the same effect. The term "mana sponge" didn't come out of nothing, after all. Now, if your healers just have regen coming out of their ears and spending more mana on you isn't an issue, well, more power to them. But unless you're at risk of dying in a few hits, you're not doing your healers any favors by stacking stamina.
Obviously all that flies out the window on any fight heavily favoring magic (which is incredibly rare) and on some 25-man heroic encounters, but, again, most people using a tool like AMR aren't going to be 25-man heroic raiders, and the tool probably doesn't go "EXCUSE ME ARE YOU PROGRESSING ON LEI SHI RIGHT NOW BECAUSE YOU NEED DIFFERENT STATS FOR THAT" when they try to use it.