Does side-channel attacks offer any difficulty to Stinson's concept of `provable security'?
Say there is a proof that a cryptosystem X satisfies Stinson's definition. An attacker builds a method to break X by side-channel attacks. Does that offer any trouble to the definition or to my proof?


Not generally: The proof covers the algorithm, and side channel attacks target the implementation. 

If someone threatens to hurt you unless (or until) you give them your private key, that doesn't violate the provable security claim of the algorithm. 

The algorithm is an abstract idea, and the provable security guarantee would indicate that no other abstract idea (algorithm) could violate the security without providing a solution to another abstract problem.


  Or would you say side-channel attacks have nothing to do with provable security?


More or less, yes; You can't have provable security against rubber hose cryptanalysis, you can't provide security if the attacker is watching over your shoulder as you perform the algorithm with pencil and paper, you can't have security if your program prints it's state at every step of the way to a log file the adversary has access to, etc.

Basically

Proofs rest on assumptions (even if they're not stated explicitly). If you violate those assumptions, then you can skirt around the guarantees provided by the proof. 

This is one reason why provably secure algorithms would ideally be combined with side channel resistant techniques (e.g. constant time code, blinding, etc) and formally verified implementations.