Firstly, a Fibonacci spiral and a golden spiral are not quite the same thing, although they are pretty close. In this image from Wikipedia, the green curve is a Fibonacci spiral, and the red curve a golden spiral, with overlapping areas in yellow:
They are close enough that for the purposes of your question we can consider them to be the same. In any case, the image provided is not close to either one. Consider some basic properties of the golden spiral, and see if they are true in the image:
1) each section is a square
2) the size of each square is in the golden ratio
3) the spiral is tangent to the square at each corner
What we can say, however, is that this is a very attractive picture of some kind of spiral.
It's also notable that just about any spiral-like curve can be made to fit within some kind of recursive subdivision of rectangles, as long as one is not too careful about the rules and does not divide too many times. For example, take this completely arbitrary spiral I just drew with my fist:
Notice how it works for about three rectangles, and then gets confused.