GitHub Enterprise is completely walled from GitHub.com (try to use your username/password from one to login to the other - it will fail).

Additionally relevant is that they aren't always identical from a technical standpoint. Updates and API changes roll out on different timelines, there are some API differences, etc. This would obviously cause problems if you were trying to access one via the API for the other.

Lastly, you have a higher rate limit on your companies Github because they have vetted you and trust you for access to their stuff. They also know who you are and have an employment relationship with you - i.e. if you decide to maliciously use these limits you will get disciplined or fired. GitHub as no such relationship with you and is tasked with managing access to the assets of 3rd parties on GitHub.com, not just their own. I see no reason to expect that your company would somehow be able to grant you higher limits on GitHub.com unless you work for Microsoft or a partner.