I believe the professor is confusing dialogue with a citation. In prose, the correct form would be something like:
"I am answering a question on Stack Exchange," said Ian Atkin.
The AP Manual doesn't implicitly have a response, but in explaining the rules, uses the following:
Jean-Luc Godard’s film “Masculin Feminin” would be cited as “Masculine
Feminine.”
Good question. I copyedit and proofread novels, so I can tell you that this is a grammatical error very commonly allowed in fiction. As you can imagine, novels allow for a bending of conventional grammar rules to account for author style and pacing. In the publishing process, editors develop a style sheet that lists exceptions to grammar and punctuation rules that should be allowed in the work at hand. Comma splices are usually one of those listed exceptions and are often overlooked in both dialogue and narration.
To comment specifically on the use of comma splices in dialogue, though, imagine reading one of these sentences if the comma were replaced by a period:
"You wouldn't like it. Believe me."
The change in punctuation creates a subtle difference in the character's tone, wouldn't you say?
The independent clauses could be joined by a semicolon, but this looks foreign and unnatural in dialogue. There is no actual rule behind this that I know of, just an overall style preference.
A more elegant way to punctuate the dialogue than with the use of a semicolon would be with an em dash. This would make the sentence both grammatically correct and still natural:
"You wouldn't like it—believe me."
Yet this also subtly changes the feeling of the sentence by emphasizing believe me. A comma does more to simply and equally link the two independent clauses.
In summary, don't look to novels to follow grammar and punctuation rules precisely; the priority in popular literature is more on style than perfection.
Best Answer
In general, No!
Your papers for English class should follow the rules of English grammar including proper punctuation. What you do as a novelist later in life is your own affair.
If the purpose of your paper is to demonstrate a particular affect achieved by bending or breaking certain rules it may be acceptable; but you must first demonstrate competence at using the language in the proper way. In many cases such rule bending is a prop used to hold up prose so broken they couldn't be sustained using normal rules. If you learn to communicate well inside the boundaries of established grammar rules, when you do choose to break them the result will be even more efficacious.