Wasn't Rutherford's assumption of gold foil to be made of single layer wrong?
You were confused about the result of the experiment. It did not measure the size of the atom, but the size of the nuclei. Nucleus is the area of concentrated positive charge in the core of the atom, and is only a very small fraction the size of the atom itself.

And the result, $10^{-15}\ \mathrm{m}$, was the size of the nuclei, while the size of gold atoms has the order of magnitude of ångströms ($1\ \mathrm{\mathring{A}}=10^{-10}\ \mathrm{m}$).

The measurement comes from the analysis deflection angle of alpha particles when hitting the nuclei. The one-layer-of-atom assumption leaded to Rutherford to use a mathematical model for one single collision to analyze the angular distribution. Because the nucleus is so small, even if there were a small number of layers, most alpha particles will still only have one collision and the result will be correct.

However, the alpha particle was passing through some hundreds of atoms and many particles actually were deflected multiple times. The calculation would be much more complicated. Even if he knew the number of layers of atoms and tried to do it the right way, he might not be able to arrive at the correct number. Of course people back then would not be able to know that, but nevertheless, the existence of nucleus is still evident and Rutherford did almost get the order of magnitude right.