> If a public repo does not have a license, it does not mean it free to copy and distribute.
Whether or not it is free to copy and distribute, it should be free to copy and distribute. (My opinion is that copyright is no good; if the file is public then you should be allowed to copy and distribute it.)
> If a private repo has an open source license like MIT, then the crawler has a right to copy and distribute that repo. Regardless if it has authorization to access the repo or not.
I should not think so. The license would only apply if you have a copy of it anyways. If you are not authorized to access it because it is private, then you would have to get a copy from somewhere else, and if nobody else is providing a copy, that shouldn't give you the right to unauthorized access. However, if it has been done, then it is done, so now there is a copy, and the license (if it is a license that allows copying it in this way) would authorize you to continue to use and distribute the copy that you have.