Healers definitelly influence and decide the outcome the most. The best healers have 80% win rate all the way till Diamond, which can't be said about dps or tanks. For experienced healer carry potential of bad players is high, and for new healers there's high probability of lose even with good dps/tanks.
And because it's such an important role, nobody wants to take responsibility and heal, they get instapops all day which is more beneficial for fast ranking even with a lot of loses. But at around platinum new healers should stop queing for XP and start doing it on a job they play the best, or their rating will stagnate. In previous seasons I've seen many healers with 800+ matches who couldn't get close to a Diamond.