From GitHub:
We claim no intellectual property rights over the material you provide to the Service. Your profile and materials uploaded remain yours. However, by setting your pages to be viewed publicly, you agree to allow others to view your Content. By setting your repositories to be viewed publicly, you agree to allow others to view and fork your repositories.
As noted in the BitBucket TOS you linked, BitBucket’s parent company similarly has no claims to code that you upload into private repos.