Here is how I've dealt with this situation.
If you have a user that you would like to be an internal tester in your organization (or the converse -- perhaps you have a client who has their own iTunes Connect account and you need access to their account as a tester or admin or developer) and they have a Gmail account, you can do the "+foo" trick on their email address, which Gmail allows through to their email, and iTunes Connect thinks it's a different iTunes Connect account.
For example, if the person I want to add is "fred@myclient.com", I would send him an invitation as "fred+appname@myclient.com", and their Gmail-based mail system will let the email through just fine.
Then, they create a new, separate Apple ID with "fred+appname@myclient.com", and iTunes doesn't complain.
Then when they receive the follow-up notification to join TestFlight, it arrives at the right email address, and when they tap the button in the email it opens TestFlight on their device, they sign in with their normal Apple ID (even if it's fredjones@gmail.com), and then they're in.
It feels a little hackish, but it works.
Because I'm dealing with this situation again with a client, I wrote up the following blog post:
http://interactivelogic.net/wp/2016/01/how-to-add-an-internal-tester-to-testflight-if-they-already-have-an-itunes-connect-account/
Hope this helps future visitors!