Nick Fury is 45 when he first meets Carol Danvers (Brie Larson). At that point in the timeline, he's already been in S.H.I.E.L.D. for years, but that's not where his career in intelligence work started.
As revealed in "Captain Marvel," Fury joined the military after graduating high school, eventually rising to the prestigious rank of colonel in the United States Army. From there, he was recruited to the CIA, where he worked numerous top-secret missions during the Cold War. This part of Fury's career is referenced a couple of times in "Secret Invasion," as he alludes to his days as a spy in the Soviet Union while chatting with Maria Hill (Cobie Smulders) in Russia.
All of that takes place long before Fury ever meets a Skrull. His career in espionage was impressive on its own, which is why S.H.I.E.L.D. recruited him in the first place. And yet, there may still be some merit to Talos' accusation that Fury rode the coattails of the Skrulls after meeting them.
Would he have found the same success in S.H.I.E.L.D. that he did in the CIA if not for Talos and his people? Would Fury still have become the director of the prestigious organization? It's impossible to say for sure. He certainly takes advantage of his alien friends — to the point of pretty gross manipulation — but he also accomplishes a lot on his own.
