Your friend is actually slightly wrong:
Healing meter doesn't matter for ANY healer.
There are a few fights where raw healing output will tell you a lot about how the healer did. However, for most fights the healing meter doesn't tell you enough to adequately say X healer did better than Y healer. There's class mechanics to take into account and within the class there are haste caps and playstyles that could drastically change healing numbers. One healer might be blanket healing while another is spot healing spike damage. Often the blanket healer will do more HPS, but the spike healer is just as important to keeping the raid alive. Unless there are GLARING differences in healing (Like triple the healing of someone else of the same class/given the same job) then don't rely on meters to guage your healers. A good raid leader can easily tell who's doing their job better without Recount anyways; Though it can be a useful tool to help pick out specifics.