There is definitely some truth in this, firstly for "set and forget" AoE heals such as Lightspring or Healing Stream Totem, which aren't necessarily standard floor-based or spammable AoE heals, but still heal smartly in the general area as opposed to requiring the player to pick a specific target. Secondly, when "spam X when nothing else is going on" is the best strategy, healing quickly becomes boring.
The problem of Atonement, and other heals
Discipline priests have suffered with this particularly in the early part of Mists of Pandaria, with Atonement being so strong, and the prevalence of Prayer of Healing spam. The problem with this is that it's really rather dull. For me at least, and I'm just one player, the fun of healing is tailoring a response to the situation. Healing is reactive, often, while you can fall into a rhythm when you know a fight well and know when the damage is coming, you're still reacting to the unexpected. And a big part of that reaction is knowing what to use.
Priests have an insanely large toolkit for different situations, it's part of what makes them such a fun healing class to play, but if Discipline isn't making the best use of those abilities, they're dull. And the worst part of Discipline in Mists has been their ridiculously overpowered nature, meaning that erstwhile Holy priests have been pushed into Discipline. And they weren't enjoying it, simply because it was boring.
If you're in a question and answer session, and the question is always "what spell should you use to heal these people up efficiently while also not wasting too much mana by overhealing" and the answer is always "Atonement", that is simply not interesting. Instead, it should vary, there should be moments of lighter damage that are covered by Atonement, allowing a Discipline priest to build their stacks of Evangelism, and have Archangel ready for the periods of higher damage. There should be times when Binding Heal is the right answer, times when a Greater Heal or a Heal are the way to go, times when it's only really necessary to fire a Prayer of Mending. The answer to healing should never be "spam this".
But Disc is far from alone in this. The original tweet to which Ghostcrawler responded bemoaned the prevalence of Holy Radiance, Eternal Flame and Prism in Paladin healing, and asserted that the single target cast time heals were useless. The same is often true for Shaman, with Healing Rain being an AoE that you set and forget, along with Healing Stream Totem, and Chain Heal spam having made something of a reappearance. As someone who doesn't play a Monk or a Druid I can't really comment on them, but I don't doubt there are situations where they're in a similar boat.
What's the answer?
What should be done? A reduction in the effectiveness of AoE heals would be a start, as Ghostcrawler hints. They are too strong at the moment, in comparison to their single-target brethren, and as a result are a more efficient way to heal at speed. What's more, smart heals are too strong, they do too much without the player even having to think of anything other than dropping them on cooldown, in the case of Healing Stream Totem and Lightspring. And Chain Heal, too, is one that does a lot of the thinking for you. I'm not advocating the removal of smart heals, just wondering if they should be toned down.
For many classes, too, mana management has become largely irrelevant, to the extent that Monks almost completely ignore spirit on gear, and have even been complaining that "their" legendary cloak is a spirit one. The effect of this on healing is that, if you don't need to worry about mana, you will go to the spell that heals the most people for the largest amount.
AoE spells should be far more expensive, in my opinion, they should be used to pad the raid for heavy damage periods, for things like Megaera's Rampages. Not for general raid maintenance. Not because they are the best answer to every situation. Not as a default. And the only way to do that is to make sure that healers can't use them as a go-to. To make them much more of a mana drain, and to make it so that healers are under pressure to use their mana wisely. It should never be the case that healers are actively ignoring spirit, in my opinion at least. If you are ignoring spirit, if mana regeneration is such an irrelevant concern, or indeed regeneration of a secondary resource such as Chi or Holy Power, then there needs to be a change. Healers should worry about mana, and if they are doing so then they will be forced to be intelligent about spell choices, and healing will become varied and fun again.
I should clarify, though, that I don't advocate a return to the earlier days of certain healers having certain roles. I don't think paladins should be a dedicated tank healer with a tiny amount of AoE, for example. That sort of class-specific niche, while it added flavor, was rather limiting, and punished smaller guilds who might not have a large pool of players to choose from, or players who play specific classes, and don't want to change.
Where the fun is for me
If you want to see what I mean about healing under pressure, step into the arena with your healer. There's never been a better time than now to give it a go. Your LFR gear is as good as honor gear, and come 5.4 you won't even need teams. PvP has never been more accessible to PvE-ers. Why am I suggesting this? Because PvP arena healing, quite aside from all the utility, is a situation where mana matters. Where every spell choice matters, in longer fights.
To me, and again, this is just opinion, that's what healing should be like. Not because I'm some elitist, but because I like a challenge, I don't like to spam the same spells over and over and still do well. I like to have to work for it, to make choices when I'm keeping people alive. PvP healing is what made me love healing in the first place, as well as PvE healing when things are rough in progress fights. Maybe it's because I play a shaman a lot of the time, and when the going gets rough is when we really shine. Maybe I'm just a glutton for punishment.