Fibonacci receiving credit for the sequence is probably due to the great influence of Western teachings in our textbooks. If India had become a great power like Europe did from the 17th century onward then perhaps more Indians would be given credit in modern text books. It seems to be another case of 'victors' writing history.  

 As for Fibonacci 'lucking out' with this problem he probably realized some correlation between the numbers and then tweaked the problem set to fit his purpose. Whether or not he just randomly thought of the correlation or was looking for real world correlations is another matter entirely which I doubt will ever be answered. There is a certain amount of credit that should automatically be given for recognizing something like that though. 

   Alex Kinney - St. Martin's University