The underlying question seems to be, "What culture gets credit for the creation of the guitar?"
Just as with border lines between countries, distinctions between cultures are artificial. Cultures interact like oil paint on a canvas: they blend together, sometimes forming new colors, other times interlacing and intertwining but retaining some degree of their own identity.
And how do we define a guitar? Different people are going to have different definitions, and each definition is going to have its own history (or, more accurately, set of histories). Even attempting to define "guitar" is problematic. Consider this: A classical guitar and an oud have much more in common than a classical guitar and an electric guitar.
There's also an implicit assumption that there must be a singular birthplace, but what we think of as "the guitar" isn't really a singular entity. It's actually a category word: the term "guitar" is a catch-all phrase that encompasses thousands of varying designs spanning thousands of incredible instrument makers.
So imagine every stringed instrument maker that ever existed in the history of humanity. Now narrow that down to the ones that had a new idea (even a small one) and executed that idea in one of their instruments. What were their birthplaces? If we could know that, we would have an answer to your question.