I'm sure there is some legitimacy to Maturi and Brewster having heated exchanges, but how many people have not had such a thing happen with his/her boss? One obvious difference is that these two are very public figures. But, as what happens in every day life with most professionals, the two individuals work the difference out, move on, and continue to work towards productivity for the betterment of team/company/organization.
Not having any inside information whatsoever, I'm sure their relationship is really not much different than any other boss/employee, with its own series of ups and downs. Theirs are just of greater interest and subject to more amateur psychoanalysis than others.