When creating Pull Requests on vulnerable repositories on Github, the snyk-bot user will generally create PRs for all Public repositories:
When creating PR's on Private Github repos, although Snyk has permission to read and create Pull Requests, the Snyk-bot does not have permission to comment and update PR's so the PR will appear to be created by a User that has permission to the Private repository.
You can control which user creates Fix PR's in Github by following this article: Integrating GitHub to Snyk via a Personal Access Token