It's true that neural networks can not be easily applied to natural languages, but there are less obvious ways of applying them (namely Embeddings, LSTMs, Attention) and provided you have enough data and computational resources they give so much better results than any other method that it doesn't even help anymore to combine them.
[1] https://arxiv.org/abs/1609.08144
[2] https://arxiv.org/abs/1611.04558
EDIT: I also don't want to give the impression that Deep Learning can solve every NLP problem. We are still far away from passing the Turing test. It's true as well in my opinion that Google's Machine Translation is oversold. It's best at what it's trained and evaluated for: translating individual sentences from news sources.
EDIT 2: There are some tasks where traditional methods can work better, e.g. text classification on long documents. That's mainly because deep learning methods are too expensive computationally.