If issue numbers are the only requirement, is it okay if every commit only includes an issue number and no text at all? If not, why not? If they say something should it be the exact same thing as the issue title?
IMHO, no. You should be able to read a commit log and understand what has been done. But if the issue titles are good enough they could absolutely be used as commit messages. Many issues leads to multiple commits however, so what you want for message is a description of the individual commit.
For larger centralized projects, I have found a requirement on issue numbers in commit messages to work well. It makes a whole lot of management issues easier.