As someone who is just beginning to think about using private repositories, if I understand correctly, they basically let you make commits in private until you are ready to open-source your app/program to the world and then, once you do, your entire Github/Bitbucket commit history becomes visible to everyone (like as if you were developing out in the open the entire time).
Now what happens if someone open-sources something before you do and claims provenance in the field/area/app/etc.? Can you basically open-source your software in return (or contact the authors directly) and "counter-claim" provenance? Obviously, the open-source person wouldn't have known about your existence since you're developing in private mode, so whose "right-of-way" would it be in such a hypothetical situation?
I can clearly see the utility of private repos for potential forking by competitors who have many more resources than you do and can hypothetically out-code you to the finish line and/or refactor your code significantly (potentially without attribution), but beyond that I don't really see much of a direct benefit to software development in private repos. Can anyone clarify the above points for me? For the record, I have investigated related posts like: https://softwareengineering.stackexchange.com/questions/87577/whats-the-benefit-of-having-a-private-repository-for-personal-projects