I would have went the other way and forced everyone to develop in public via github (or similar, in fact it wouldn't need to be private if Coursera had access to the git repository). I'd guess it would be more work to try and painstakingly recreate a unique and authentic looking sequence of commits than it would to just do it yourself, probably teach some good habits too.
Are your downvotes coming because of you specifically suggesting github or are they because of the underlying idea? I think the idea's good. I had a group projects in a coding-intensive course (not distance) this summer and one of our members procrastinated endlessly. He kept insisting he'd done work and we hadn't but he was new to version control and didn't realize that you can pull up commit logs. He quit the team when he saw them.
At the least, if someone contributes a ton of code for an assignment in one shot that's identical to somebody else, the professor could compare commit logs there too. Tons of code is out there on the internet and plagiarism is something that'll be tempting on the job under a deadline, too, with potentially more serious legal consequences.
I keep my code private until the class is over, then open-source it. I consider this stuff to be my resume.
