The badges of employment versus self employment are well established before the Courts. In the vast majority of instances it will not be difficult to determine status. It would be ridiculous to argue that all FIs should be employed or self employed.
There are many features of the work undertaken by a FI and his relationship with school(s) which would dispose to the possibility of either arrangement.
IO540
On a minor point of order you dont deprive yourself of being able to fund a pension as the current rules only take account of your employment history in the run up to obtaining pensionable age. That said, there would be some that would question the benefits of funding a pension these days!
You are otherwise correct in your comments.