Yeah, good question! Alas, it’s just a flaw in the puzzle — based on the information given, it totally could be the 46th rather than the 47th. (You can even make a puzzle out of selecting starting numbers other than 1, 1 which result in the 45th begin the first over 1 billion, and the 46th being the first over 2 billion.)
Or, to disambiguate, you can include the info that the 45th Fibonacci number is “just over 1.1 billion.” Then, if you assume the 46th number is over 2 billion, and work backwards to find the most recent terms, you’ll pretty quickly get a contradiction (44th = 46th – 45th, so must be over 800 million; similarly, 43rd must be under 400 million; but then the 42nd must be larger than the 43rd, which doesn’t make sense because the sequence is increasing by construction).
