Is using "have" better than using "got" in the following sentence?

"Have" is correct and can be only one thing: I possess/hold/etc. the file.

"Got" can be two things:

• I've got the file: has the same meaning as "I have the file", but is somewhat informal; if you leave out "have/'ve", it is very informal (in this case, "got" is the past participle of "get").
• I received the file (in this case, it is the simple past of "I get").

My guess is that your corrector either found "got" confusing, or took it as "have" but considered that too informal.

Both are correct grammatically, but mean entirely different things. "I got X" means "sometime in the past, I came into the possession of X". "I have X" means "I currently posses X".

Consider an extended version of the same: "I got an MP4 video file for Christmas". Some might argue that there are better ways to express the idea, but there's nothing terribly wrong with this one.

Perhaps not as useful an answer, but I still recall my English teacher told my class in no uncertain terms that there's always a better word than "got".

You can not use got on its own as a present tense meaning 'have' or 'has' in standard English. Say that someone has something or has got something:

We've got (NOT We got) some ideas.