Doesn't it strike you odd that out of everything Scott could have picked, he picked a puppet-like character? My guess is that the Puppet is somehow using the toy animatronics in the 2nd game (the ones that might not have dead kids in them) and controling their bodies like a puppeteer. Why do they fall for the Freddy mask? Because without that mechanic, the game wouldn't be so hard? Now I'm doubting myself.
But tell me why you think the Puppet is a Puppet, or is even existing, in the game down in the comments if you have any.