You're both wrong, OP. Healing meters are not the end all of deciding who is a good Healer - however they can be a very effective tool if used properly. Unfortunately, in my experience, most people use them improperly.
Raw HPS and total healing done is a very innefective tool as it is very subjective. Fight mechanics, healing assignments and many other things skew it in unproductive ways. Holy Pallies are going to wreck meters on a fight like Patchwerk. Does that mean they're better then your other healers? Nope. It just means they have the right tools for that encounter.
On the other hand, saying things like "Welp, my assignment didn't die. I'm doing great!" is just as idiotic. You should always look for ways to improve yourself. Sure your assignment didn't die. But if you and your other healers did a better job managing mana and CDs, could you drop a healer and add additional dps? This is the kind of question you will never be able to positively answer with a "good enough" kind of approach.
Only idiots look at total healing instead of effective healing.