I often see something like "A Ms. Smith states that...". Is using "a" before a person's name grammatically correct?
Sure. There is no guarantee that the name uniquely identifies the person. Consider "a John Smith." Until you have identified the particular person using that name in that situation, the indefinite article remains appropriate.
I've always associated this sort of thing with a level of obscurity. So, for example, if someone is relaying a message they received via the telephone. "Sir, a Mr. Rochester called. He said he'd like to meet this Saturday." This implies that the message-giver doesn't know who Mr. Rochester is, or has reason to believe that the "sir" may not know who Mr. Rochester is. As opposed to just saying the name: "Sir, Mr. Rochester callled. He said he'd like to meet this Saturday." Leaving the "a" out of the sentence makes it sound more certain. Clearly, the message-giver knows, and expects "sir" to known who Mr. Rochester is. That's my interpretation of it, anyway.
