What I'm thinking is that wordpress is looking in your two folders 'atahualpa' and 'atahualpa373' and one of them is not the latest so WordPress is saying you need to update.

You can keep each version in it's own folder and run 3.7.3 If you find an issue let us know.

I had that issue where I had both 3.7.1 and 3.7.3 installed and I was seeing an update prompt. Once I deleted 3.7.1 the prompt went away.

Ok, now i try in my local backup.

Ok! It's easy to fix, just renamed old folder "atahualpa" to "atahualpa-old" and now it's ok, i don't see the update available. Btw, surely i can also delete this folder, but at the moment i like to maintain all versions, for security.

Btw, it seems that Atahualpa 3.7.3 works fine with Wordpress 3.3. I have updated my local backup without problems.