As long as Fischer does not suspect that he is dreaming, he cannot "connect the dots" and realize that one of the men that kidnapped him in the first dream was Saito, who sat next to him at the airplane.
I amend my previous answer to better reflect what is going on with the movie.
Fischer boards a plane to LA to join his family for his father's funeral. In the exact same plane, Cobb, Ariadne, Arthur, Saito, Eames and Yusuf are boarded too and they are all sitting in nearby seats. Fischer knows that he is boarding the same plane with his business opponent, though he doesn't quarrel with him; Saito hasn't initiated yet his plan to destroy the former's company and even if he did, Fischer wouldn't do anything other than maybe ask to sit in a different seat, away of him.
By the time they enter the first level of the dream, Fischer meets Saito, Eames and Yusuf in the taxi. He does not even remember Saito but he also fails to recognize everybody else, though moments later he sees them sitting next to him at the real plane. If he was to understand and question Saito's motives, then the same applies for the other two.
I think that, although that it is not addressed in the movie, Fischer could only understand that something is going wrong in the early levels. As they are entering in deeper dream levels they are also diving deeper into his subconscious. Fischer only focuses on his ultimate target (to find what his father left him) which obscures anything other that might be considered irrelevant (his company, his whereabouts, what the others are telling etc).
By the time they are at the third level (where everybody is on Fischer's side), he does not seem to question why Saito, Eames and Arthur aid him, though in a previous dream they kidnapped him. That brings us to the conclusion that he cannot recall this previous knowledge. He is dreaming. He cannot persevere the full dream spectrum neither can he remember the previous dreams and what was going on then. And if we go one step further, he cannot recall his reality, either. Dreams are shaped of what interests us and sometimes they are influenced by what we have seen prior to falling asleep. As a common person would not rationally think that "what I am seeing right now is influenced by what I saw before I went to bed) then the same applies to him.
Keep in mind that, at the baggage pick-up point, Fischer seems to recognize who Cobb is, though he quickly turns his head away realizing that it might be a "deja-vu" situation. If he cannot recognize him, with whom he actively shared merely 3 dream levels (second, third and limbo), then in a similar fashion he wouldn't be able to find out who Saito is.