Is Unification “an Implementation of Existential Quantification”?

Question

I read a comment (I've forgotten the source), "Unification is an implementation of existential quantification." (Emphasis mine.)

If true, this point of view clears up many things.

For instance why omitting the "occurs check" in unification can lead to unsound inference: it would be the same as using the assumption of the existence of a thing in your proof(-term) of the existence of that thing.

It would also explain why the algorithms for unification in logic programming language engines I've looked at seem (to me) more arbitrary than other operators such as conjunction and disjunction.

But - is the statement true? Is it an over-simplification?