The problem with healing in 4e is the FLUFF. 4e incorporates the somewhat odd notion that all 'power sources' need equal access to and effectiveness in all roles. And therefore we have the Warlord who can yell you back on your feet after you somehow survive swimming a river of lava with -2 hp.
If that healing was fluffed as magic spells, divine grace, healing herbs, alchemical potions or the tears of unicorns then no one would have a problem with it.
However we are all pretty certain that a pep-talk does not outweigh 3rd degree burns. And if you swam a river of lava and got reduced from 145 to -2 hp it was not luck, it was not morale, you got roasted alive and are a hideous husk of burnt flesh clinging to life by sheer determination.
Yes, in reality healing from that would take months in the intensive care unit, and your odds would not be good. But a month of bed rest is less offensive to that violation of veracity than a quick atta-boy and a good nights sleep.
And magical healing? Why wouldn't it work? It's magic after all.