Does Naive Bayes Classifier require assuming a specific distribution for training? Since NB is a generative classifier, we assume that the data points are all generated from a distribution, right?

But since we can compute the MLE of p(x_i|y) by counting (MLE of p(x_i|y) = # of (x_i,y) / # of y), do we really need a specific distribution, if at all, to model the likelihood(p(x_i|y))?
The most harrowing problem would be "interpolation". That is, computing $p(x_i | y)$ for $x_i$ and $y$ you have not yet observed, but fall within the convex hull of your observations. 

You have to bin events together, or come up with a wacky interpolation scheme. This does work. However, If you assume a distribution, $p(x_i | y)$ becomes continuous, and you end up with a more statisically sound means of interpolation.