Given that similarity-based learning requires a distance measure in the feature variable space as well as a ground-truth set of input-target mappings, is the following statement true or false?

In the case of a KNN (K=1) classifier based on the cosine similarity distance measure, the model (the KNN classifier) always predicts 0, if the query and existing nearest neighbour are the same and it predicts 1, if the query and existing nearest neighbour are different.