Felipa:
My reasoning is sound, even if it doesn't agree with your preconceptions.
As long as the Newark school is linked with Lincoln College then they can only get visas for their student via that establishment. And if Lincoln College lose their status then that has a knock-on effect.
If the Newark School had not had a link to Lincoln College the students would not even have gone this far.
A possible change to getting Hull Uni to oversee the course would possibly give the school a better link, and chance of survival as an international supplier, but you seem even to be against this.