No this one is not a fake.

But since you brought it up this series is full of fakes. In fact most of these stamps were hand canceled. Unfortunately hand cancel inks generally were not indelible. Thus you should really look over any of the classics very carefully.
Can you see the removed hand cancel in this photo, look at the red arrows. This is why I am against the cleaning of any stamps.
The link will give you more detail and the photo of the Scot #1 stamp.
http://www.theswedishtiger.com/remove.html