That's a neat observation! But isn't it for the naïve reason that, with negligible overhead, the run time of executing `fib(n) = fib(n - 1) + fib(n - 2)` is the run time of executing `fib(n - 1)`, plus the run time of executing `fib(n - 2)`?
On the other hand, if someone had asked me for an estimate on the run time, I probably would have tried breaking out the master theorem instead of thinking of this, so I don't want to downplay the observation.