Constructing a training dataset is a separate problem. You could potentially crowdsource enough negative examples. Once you have the dataset, a neural network would most likely be able to learn to classify sentences with a reasonably good accuracy.

Unlike current DL models, humans have a world model (common sense) which is formed through an ability to create/update/lookup explicit rules/facts. Once we figure out how to incorporate that into a learning algorithm and/or a model architecture, AI will become a lot smarter.