Well, technically they are different Links from the same timeline, but despite that, they are visually identical and the same character model.
The point is that seeing Toon Link appear as decoration on the stage made us think he might not be playable and be cut in Super Smash Bros for Wii U and Nintendo 3DS because he is a "clone". This was of course false and that may be the case here with Paper Mario stage.
Having Palutena's Temple does not imply Palutena has being playable anymore than Wily's Castle or Tortimer Island imply that Dr Wily or Tortimer are playable. Same goes for Mario Galaxy with respect to Rosalina. Regarding the Boxing Ring, Sakurai deliberated took out all references to the WVBA and Punch-Out!! when he initially revealed this stage to throw us off. For this stage, he flat-out said that this is a Paper Mario stage.
Though, like I said, I think Spirit Tracks is a great counterexample because Toon Link appeared on that stage as decoration early on. Many saw this as deconfirming playable status. Maybe Paper Mario will be a similar situation, where his stage is revealed before his playable status. I doubt it, but I hope my doubts are proven wrong because I enjoy Paper Mario, both the character and the games.