When an experienced English teacher, a native speaker, says that something is correct and gives a reference from a dictionary, it is not exactly tactful to suggest that your answer is better. If you thought that, there was no need for you to post the question in the first place, or for the teacher to spend time on a response.
Hello, I am not a native speaker.
I happen to have a book called A dictionary of Modern English Usage, written by H.W. Fowler. I refer direct to it and saw the following words. I shall write them down here and hope it may help.
direct(ly). The right adverb if straight is meant is direct; directly should be confined to the meaning of immediately.