FIBQ , how to calculate intermediate nodes value in segment tree

I am trying to solve FIBQ
using the editorial editorialFIBQ. Can anybody explain me why we are calculating the
L.sfibm1 = Fibonacci(A[i] - 1)

L.sfibp1 = Fibonacci(A[i] + 1)

If the input array is 5 ,7,8,10,12.
then fib(5), fib(7) , fib(8) , fib(10),fib(12).
then for intermediate nodes fib(5+7), fib(8,10),fib(5,7,8,10), fib(5,7,8,10,12).
Now merging logic for 5 and 7 can be simply fib(5+7). then we are using such complex logic as explain in editorial.
Please explain.

Please go through this.

Hope this helps