Having started FFXIV in Gridania in both 1.0 and ARR, and played through the 1.0 Gridanian storyline I can definetely attest to just how dangerous and powerful the elementals really can be if really provoked, it is not an exaggeration on Gridania's part.
Some aspects were kind of taken out of proportion by Gridanian citizens, but the fact remains they were powerful entities that could turn the whole forest against anyone or anything it viewed as a threat, with the idea of exactly what it was that they percieved as a 'threat' seeming to be somewhat unintelligible to normal mortals, even going so far as turning someone to stone (it happened to a boy named Khrimm in 1.0's Gridanian story after he set a Hedgetree on fire simply to 'prove' the elementals were fake, and that single elemental was so furious it scared the other elementals into authorizing the Wood Wailers and the God's Quiver to destroy it for the well-being of everyone, and Amberscale Rock has a story connected to it that it was actually a dragon that had been imobilized by the elementals). Emphasis on were.
ARR's storyline outright says that all the recent incursions and transgressions into the forest by people and entities that the elementals would not have even thought twice about punishing before the Calamity the elementals appear to now turn a blind eye to, and it was confusing and terrifying the Gridanians that they were doing so. The Calamity seems to have changed the aetheric makeup of Eorzea and resulted in a massive powering down of the elementals to the point that not only do they not even show themselves generally anymore (unlike pre-Calamity where they actively roamed around the forest - they were actual random enemies you could fight), they seem rather powerless to stop even Ixali incursions into the forest and outright poaching of trees, requiring them to appeal through intermideries like the moogles and the Seedseers for help to neutralize these threats. And then there is also the little problem of Ascian medling in the whole thing too.
So basically the elementals do exist and are as every bit powerful and terrifying as they're made out to be, but, due to the Calamity their power has waned considerably to the point they're no longer really capable of exerting much force of the forest or Eorzea in general (an overlooked fact that was more stated in 1.0 was that there are elementals in everything including rocks and the air, and that they're found all over Eorzea, but were always far more numerous and potent in the Black Shroud for some reason).
As for whether the elementals could ever repeat the Great Flood? Hard to say, especially with their aformentioned weakening. But you also have to remember that back at the end of the Fifth Astral Era the level of aetheric abuse through the magic unleashed during the War of the Magi was at such a level that the elementals thought that destroying everything with a flood was the only way to save things, not helped by one of the instigators being right on their doorstep (the Amdapor).
As the elementals couldn't even stop the Garleans from building a base in the middle of the forest after the Seventh Calamity, I don't think the elementals are now in a position to cause a repeat of the Sixth Calamity, even if they wanted to.