It's not a war of words, but rather a sentiment that will continue to be expressed by both sides. Kirk Cousins reiterated to Sal Paolantonio that his desire has been to remain in Washington for the remainder of his career.
The Washington Redskins have said, and will continue to say, that they want Cousins to stick around a long time as well.
But actions will speak volumes on both sides. I don't doubt the sincerity of what Cousins or the Redskins say about one another. It's also more complicated than just saying what your desire is; Joe Gibbs once said he intended to stick around beyond his fourth season of his second stint.