I agree with you but I also think it's deeper than this. Mourinho pioneered a lot of innovation in training and football style during his early career but it was denigrated by a lot of people. Pep has always been the darling of the tacticos who is celebrated for his influence in "playing the right way" and convincing whole generations of coaches into that ideal. 90% of coaches in the PL for example idolised Pep and adapted his methods. His impact on football as a whole is treated as monumental, almost like there's a pre and post Pep era in coaching.
Mourinho legitimately is a world class manager. His winning record is incredible and his innovation undervalued.
But he never recieved the credit and widespread acclaim that Pep did for similar successes. He's always been bitter towards Pep for numerous reasons but I've always felt this is the biggest one.
Pep, Klopp and Mourinho are the coaches that have defined the last generation in terms of tactics and Mou is seen unfairly as the red headed stepchildren in that triumvirate.