This is misleading. Of course your healers need gear, they just don't need the new gear while first processing in an new raid first.
This gearing strategy only works if you stay around after the progression and make sure they catch up gear wise - which is something that might not work in casual raids (it might work but those whoe already got gear will most likely complaind, be inattentive, or even fail to show up), thus this gearing strategy is not recommended for them.
It also assumes that your raid group makes less mistakes than the encounter is balanced for in regards to healer output, which is most likely true for the progression guilds, but for many others it might not be true. Gearing your healers up first can be advisable if your raid likes to stand in the fire.