I did not see the tv program, so had better be careful what I say about Nev and possible motives.
However I worked at NJS for nearly 10 years, and while they were not always squeaky clean in their treatment of some staff, I very much doubt that they would pull a dismissal solely on the grounds of a tech log report regarding fumes. I had several occasions to ground aircraft, though never for fumes. Usually I stopped when I considered that the MEL had been abused a bit too much eg rotating defective components for 'trouble shooting' when they bloody knew that the part in question was cactus but did not have a spare. I also wrote up fumes when cabin crew or passengers complained, as we were encouraged to do during the investigations which went on for some time.
Never once were my write-ups or decisions to stop the aircraft flying questioned by management, at least not to my face.
I suspect that the problem in this case may run a bit deeper and maybe they are right to lay off staff who have an allergic reaction to the much maligned 'gas chamber', if only to protect both their shareholders and their customers.