Gaussian distribution with a zero mean...

Indeed your are correct that one can have a Gaussian distribution with a zero mean, but that does not apply in the situation we are dealing with here. The essential characteristic of the Gaussian distribution is that of symmetry. It is symmetric about the mean. So if one has a zero mean, there must be just about as many negative values as positive ones, and in our case there are no negative values. Now that doesn’t stop people from using what is called a truncated normal distribution when there are no negative values, but this must be distinguished from the Gaussian. If you cut a sphere in half, you end up with two hemispheres—you would no longer refer to them as a sphere, although the shape is still spherical.

By the same token, the truncated normal distribution may still be useful, but there is no theoretical foundation for it. We all know that the Gaussian distribution is much abused in practice, and this would be yet another case in point. One could not have a better case than the one at hand, where the Gaussian was relied upon in an obvious case of power-law distribution. These two distributions could hardly be farther apart in their essential characteristics. The Gaussian is the tightest distribution found in nature, whereas the power-law distribution is the broadest