I had this happen to me earlier today. "Just DoT and heal" - DPS and tank. This person is also the one who doesn't really mitigate damage. It was at that point I knew they didn't really play healer and doesn't understand how much DPS a healer can output.
It's completely fine to leave them at a lower health. In fact, as you get more accustomed to healing, your baseline of keeping everyone at a certain point generally gets lower and lower for regular content runs when you have strong oGCD heals or powerful GCD spells that can be instant cast on the fly. All you really have to do is be aware of possible mechanics that hit heavy and be ready to heal before it hits and let the regen do its thing after. The other times you can be using that to spam your attack.
In fact, some jobs actually require your other characters to suffer to get the max possible benefit. That's right AST, I'm staring at you (Essential Dignity scaling to 1100 at 1 HP). So yeah, don't listen to people who don't tell you otherwise.
Just ensure your baseline isn't too low where if they die, it isn't your fault and it's all good. If it's a mechanic they didn't respect, that's entirely on them. A Healer's mana is too precious to be wasted on someone who doesn't respect the mechanics.