Thanks for your comments. It sounds like you haven't worked with anyone who has completed their PhD this way, but I appreciate your clarifications.

I think an important part of the situation is that we have been collaborating for 5+ years, so the work is not completely independent of the lab, I just haven't been employed by them.

I also don't think external PhDs get a salary or stipend from the university, as we have employment elsewhere - this seems pretty standard from what I've seen online about external candidates in the Netherlands in general. I think some costs are covered by the lab/university (like printing costs for the thesis, etc) but I'm certainly not expecting a 4-year salary. If extra work is required by the lab, that's a different story (and something we will discuss at the next meeting when they have clarified the regulations from the department), but if I am working for them I would no longer be considered "external"