Lindsey being impossible to work with according to Ms. Nicks is a reason to fire him, how? What is she,
a kindergartner?
I would hope we do not live in such a callous world where from one day to the next your near and dear long time colleagues or friends or business partners and co-creators go" I don't want to work with you nemore, BYYYYEEE!"
If they come out with: " We cannot work with Mr. Buckingham anymore because: he should be in rehab due to his habitual 5 pints of Tequila a day/ his constant threatening us concrete bodily harm by bringing pistols to the studio and aiming them at us/he has a contagious skin disease and refuses to wear clothing/ ANYTHING valid!
Scheduling conflicts can always be worked out-- Mz. Nicks there sure has been the cause of such on plenty of occasions.
Just saying "cause we don't like you no more"
smacks of two year olds.
That kindergarten level of functioning also, imho, holds for your statement that "they are a rockband and can fire whomever for whatever reason they choose."
They are a Business. With people with 30-year or more, tenure, contracts, and commitment. They are not a playground random bunch who take the ball home.
BUT! Seems I am wrong, and really, that is EXACTLY what they are. 
Hence! have fun with them, those who still want to, but do not come blame those of us who are stunned and deeply shocked by the level of immaturity displayed, I'd say.