I've been in my share of these situations myself. As a healer, you have to get accustomed to it. Your leaders will ask questions, and they'll often reach conclusions based solely on hard data, without any thought about the circumstances. Data only tells one side of the story. Context is just as important.
From your perspective
So thinking back to the original scenario, you're essentially down to two options. Granted, you can rely on your other healers; for the moment, we are focused on you and what your options are. You have zero cooldowns available. Your options are to either eat the damage and keep your tank alive, or be a good raider and run out with the rest of the team, potentially condemning your tank.
If your tank falls, it is a wipe.
I know that in an ideal situation, healers are constantly aware and will always have a response ready for the tank. That tank would never fall into the red in the first place. Situations aren't always ideal, and you're not always going to have the perfect attempt.
I was in a situation once taking on Sindragosa in heroic. I had just gotten pulled in with a Blistering Cold. The tank was low, the raid was low and it looked like we were going to wipe. I ended up lighting a Guardian Spirit on myself and unloading a Divine Hymn in desperation. I took a lethal blow, but the ability kept me alive. Naturally, this makes me look like a baddie -- but it was either that or lose the raid.
The priority here was to keep the necessary players alive. Typically, those tend to be the tanks. If you die, your raid can still carry on. With druids or well-planted Soul Stones, it is possible to recover. If your tank dies, it is a wipe, straight and simple. As a shaman, you don't have an out. Actually, I suppose you do, if you keep keep your Reincarnation handy. It'll be a clutch move to intentionally eat a death and then pop up when the coast is clear.
From the leadership perspective
In a progression guild, you're looking to keep everyone sharp. Having disconnecting players? Players who seem to die on every attempt because they're slow? Can't get out of fires? If they show no signs of improvement, then you don't have much of a choice. You have to cut them. A raid will only progress as fast as the slowest player.
Evaluating healers tends to be a process that takes longer. One of the key attributes you want to focus on is player skill in addition to numbers. Naturally, a recruit healer who makes the conscious decision to stay in, take the hit and keep the tank alive is something special. But looking at combat logs or meters, you'll see someone who was slow, stood in the fire or did something else. Context is always important.
The full story is always important. I try to make a habit of delivering a quick recap on the events that led to a wipe. Keep an eye on your healers. You can't really gauge them after a raid or two. The best you can do is try to distinguish between a genuine fail versus a non-genuine fail. Keep track of them as best as you can either by writing down the circumstances or relying on your memory.
So going back to the original question, if you're going to get fired after one transgression, there isn't really much you can do. You tried to do your best. Besides, if that guild is going to can you after you tried to keep the raid and tank alive, then you won't want to hang around them, anyway.
Of course, the best case is to not get in such a situation in the first place. Keep those HoTs and heals on your tanks as much as possible so that you do have that buffer. Better to not have to decide between your well-being and that of the raid.
Need advice on working with the healers in your guild? Raid Rx has you covered. Send your questions about raid healing to email@example.com. For less healer-centric raiding advice, visit Ready Check, and don't miss our strategy guides to Icecrown Citadel and Halion/the Ruby Sanctum.