Is this an independent clause?

[lccseschroll]

I was observing a 9th grade English class today and the lesson was on commas. The teacher had a sample sentence and labeled it as correct.

I wore a hat today but he didn't.

Students thought a comma should be placed after today. The teacher said no because "he didn't" is not a complete thought or independent clause. The students argued that it is a complete sentence/thought. She clarified by saying that it does not answer what he did not do.

I questioned her after class and she held that it is a fragment, one that we often use in casual writing and speaking. For formal writing, it is a fragment. She stated that the text they use would categorize "he didn't" as a fragment.

I'm still not convinced. I think it is a complete thought/sentence. What can you tell me?

[borat]

i agree with you that it is complete. there should be a comma.

subject/verb is a perfectly acceptable complete sentence. "He did." We were always taught that a new subject (he) is a good indicator of the need for a comma.