A Few Ticks of Avoidable Damage

If the damage is unhealable, they will die whether you heal them or not. If the damage is healable, and you decide not to heal them, you are not doing your job. It's not burning mana unless you are mana starved by the end of the encounter (in which case, it saves mana to keep DPS alive to end it faster). 

sorry but there is a lot of damage in the game that is meant to be avoided.  I can spam fast expensive heals and keep someone alive through Iron Qon's spears for instance but I will go out of mana and the entire raid will likely wipe.  WoW accounts for sale

Or, I could stop healing someone and we could finish the kill with 9 people or 23-24 people, whatever.

Sorry, but a healer healing through bad will go out of mana far quicker than an extra dps would save on the kill time.  It's not even close actually.

There's a vast gulf between someone getting snippy and self-righteous about healing one or two ticks of floor fire off that one guy a few times, and having to desperately spam heal the guy who's been obliviously standing in the fire for the last 45 seconds.

Most people are talking about the latter...

The latter leads to an attitude that makes the former into acceptable behavior. If a 25 man raid is dependant on your heals, alone, then there are far bigger problems. 

6 healers in a 25 man will either a. not be able to keep someone in the fire alive on Iron Qon for longer than 3 seconds or b. have no trouble keeping him alive for the fight, depending on the difficulty. Either way, the correct course of action is always to try. 

I heal people through a few ticks of avoidable damage because I don't expect everyone to have fast reaction times or to even know the encounter mechanics (especially in LFR).

Like you say though, if they've been standing there for a while in a puddle and haven't moved then I have to give up trying to keep them alive.

And if you're not mana starved at the end of the fight your team could do with fewer healers. As a healer I will definitely heal a DPS who gets caught in the bad for a good reason. And I'll even waste a heal or two on "stupid," Where to buy wow accounts but only when priorities and mana pool allow. Being a team player includes bringing everything you've got.  Part of the job of DPS is to stay out of the bad, use your cookies, stand in the healing circles of goodness as possible, and use your defensive cool downs.