spin = fabricate?

No. Genuine spin is not a fabrication. It just portrays an event in an extremely positive manner.

Here's an old joke to illustrate the idea.

There was a footrace staged between only two countries: the U.S. and Russia. The Russians lost, but they applied a little spin. As they reported the story, The USA finished next to last, while the Russian team finishe in second place.

Second place sounds pretty good, if you forget there were only two teams. Notice they didn't lie or fabricate anything.

It seems we all apply such little spin quite a lot.

Of course we do. Most people hate to tell a direct lie, but I doubt I know anyone that doesn't apply a little spin, misdirection, or at least allow us to draw false conclusions.