Realistically if you just want to try out someone else's contract in a safe environment, the existence of the test nets is entirely irrelevant.
The contract is going to be at a different address, all the accounts involved are entirely different, the state of the contract is different. Even proving a contract at one address is the same as the contract at another address is non-trivial.
Pretending the existence of a test net proves anything is a lot like pretending the availability of source for your OS, compiler and dependency stack proves something. Maybe possibly for a professional with unlimited time, but that's it.
The contract is going to be at a different address, all the accounts involved are entirely different, the state of the contract is different. Even proving a contract at one address is the same as the contract at another address is non-trivial.
Pretending the existence of a test net proves anything is a lot like pretending the availability of source for your OS, compiler and dependency stack proves something. Maybe possibly for a professional with unlimited time, but that's it.