It's true and this is one of the biggest problems with healing.
To start off, there are obvious times when it is the healer's fault and there's no denial. Sudden AFKs, being undergeared, whatever, obviously those are all the fault of the healer. That's really nothing special.
The bad part of healing is that everything else also becomes your fault.
DPS and how it is your fault
DPS is low so the fight takes too long so you go OOM: Get better gear or heal more efficiently.
DPS pulls aggro and dies: Heal them, shield them, bubble them, there are ways to save them.
DPS dies in a fire (don't we all wish?): Heal them, shield them, save them.
Tanks and how it is your fault
The tank can't hold aggro, DPS dies: See earlier case of DPS and aggro.
The tank is undergeared, takes too much DPS, and dies: Get better gear or spam more and he'd live.
The tank is undergeared, takes too much damage over the fight, so you go OOM and he dies: Heal more efficiently or get better gear.
As a general rule, death is caused by a lack of health and healers are the best at increasing health, and therefore preventing death. Ultimately just about any death can be blamed on a healer.
I don't intend to blame healers for everything, but instead just to point out that the mistakes of others are passed by the game onto the the healers. Every 'challenge' in the game tends to involve either someone taking extra damage or dying, and except for a very few strict DPS-limited fights (Thaddius is the only that I can think of, even Gruul could potentially be solved with better healing), all fights ultimately shift all burdens to the healers.