The fairy doesn't show up as a party member, so it IS difficult to tell if a SCH is doing anything in pre-30 dungeons because the SCH has no SCH-specific skills to use. Hence using DPS skills more than healing skills gives that impression. Though it should be pretty obvious that you're healing people if they aren't taking a dirt nap.
That said, it is also obvious when you aren't healing them because they won't hear the "targeting" tone or the line that shows up when a cast starts.
I'd rather healers not try to heal with CS on because it just makes them look incompetent. DPS'ing without CS, fine, because you might not have CS as a SCH in the cross-skill set. SCH is far far easier to do DPS and just straight up ignore healing requirements, which is partly why other players might think the healer is being lazy or incompetent.
That said, if a WHM is DPS'ing and not healing, it's VERY obvious. Because the tank will fall over in 10 seconds. SCH's Eos/Selene will never let the tank die, so the only way the tank dies with the fairy summoned is by the tank being farther than 21yalms away, or the tank standing in every AOE without stunning the boss's powerful attacks. In harder content, clearly the fairy can't solo-heal a party because you don't have control over who she targets without micromanaging.
What I find is that if you play SCH, DPS players (particularly SMN and BLM) will heal themselves more frequently than when I play WHM. That's all fine, but that just shows how inefficient healers DPS'ing really is, because it brings down the total DPS of the party if the party members are stopping DPS themselves to heal. If SMN and BLM's are doing this because they always think SCH's are incompetent, what does that really say?
As WHM, unless I get a really good tank, it's usually cure I/cure II on the Tank, and cycling to the DPS if they happen to take more than 10% damage. There's usually no possibility of DPS'ing unless the entire party is avoiding damage and not speedpulling. On SCH however it's Aldoquium/Psysick when the target has taken at least 30% damage otherwise adloquium is wasted. Eos/Selene however won't let most of the party lose that much HP. So the SCH dpsing is simply "doing something" other than standing around waiting for someone to take enough damage to actually heal efficiently. Since they can recover 20% of their MP every minute from Aetherflow, there's minimal risk in running out of MP unlike WHM.
If players are playing the dungeons like they are designed, healers would not be DPS'ing at all except when the party is taking no damage. DPS and Tanks would never heal themselves or cure themselves of debuffs if they were playing the game as designed too. But that's rarely the case. As WHM I've seen tanks cure themselves if I waited until their HP lost was enough to justify Cure II during normal pulls, but when speedpulling, I've seen more tanks wipe because they lose 6000hp in a single hit. Even Divine Seal+Medica II+Regen+Cure II doesn't recover that much damage continuously without relying on crits.
When in doubt, don't step out of your role unless you're taking ownership of the party failure for doing so. It's far easier for the healer to not DPS and just save their MP until someone needs a heal than it is for them to DPS and cause an overall net DPS loss because the DPS players think the healer is incompetent and are healing themselves. You will have people that will complain either way, so justify what you're doing instead of just letting the DPS walk over you.