I see what you mean. You can use a hash function to build a PRNG, but the hash function itself it not a PRNG.

In a hash table, the hash function is not used to produce a series of random numbers, that's why it's a bit silly to call it a PRNG. Instead, the purpose is to reduce a (possibly larger) input value to a fixed size output value, often with the requirement that similar input values should result in very different output values to avoid clustering.

However, your hash table example is still useful as an analogy.