Fredo probably had accumulated some independent means over the years, Cristina. I think Michael's speech was more about firing Fredo from his life than firing Fredo from his jobs in the family.
The more revealing aspect, IMO, is Michael's sense of possession. He says to Fredo, "...I don't want you near my home" [emphasis added]. Not "our" home. I always thought Fredo and Connie lived (or had lived) on the Tahoe compound just as if it were the Long Beach "Mall" in days of old. But Michael owned it. He does acknowledge that he and Fredo share a mother ("When you want to visit our mother, I want a day's notice--so I won't be there").