No, it's not overblown. Head over to FFlogs, pick a fight, and look at all the healers. AST is always the lowest by a significant margin. Their personal DPS is the weakest in the game. The exact amount varies by which encounter you look at, but it's pretty much always at least 25% (and seems to be even higher in Rabanastre, which could be due to who is doing that regularly vs savage). It doesn't tend to matter as much in group content because cards and they can push a lot of HPS.
But I find playing AST outdoors downright painful.