"The" Before Initialisms and Abbreviations

I posed this question to the Chicago Manual of Style:

Q: It sounds natural to say, "The diplomats met at the headquarters of NATO" (the North Atlantic Treaty Organization), rather than "at the NATO"—even though the latter seems technically correct.

On the other hand, some might say, "I consulted the CMS" (Chicago Manual of Style), rather than "I consulted CMS."

What guidelines apply here?

A: We just write it the way we say it. As a result, different writers might phrase it differently.