The scenario is simply: you perform some action on one service and then some entity has the right (or might) to demand from you the private key with which that action was performed, but not "give us everything you have."

The equivalent when the scenario is an attack, and not a legal game: some entity manages to hack your computer with which you access the service A and on which you have only the private key for A, but not your another computer with which you access the service B, with the another key.

Separate keys: just your access to the service A is compromised, one key: all accesses are compromised at once.