Nope. In fact, that was one of the things that pissed the purists off, since the Elves never took part in any human battles after the Last Alliance. They were busy fighting up north, in Lorien and Rivendell, where the fight was down to them against the orc forces.

As far as I can tell, they're pissing into the wind here. There is no way they can prove this claim, unless they make some vague claim about being influenced in some way by the other books. But that's easily countered by saying that the filmmakers were making up stuff that had to fit into the same world, so it's inevitable that some of it might sound like Tolkien's other writing.