The argument is for deterministic environments--no initial condition dependence.
If initial conditions are allowed, then you can consider the following environment: initial condition is an arbitrary source-code; the environment proceeds to implement said source-code. Clearly this "environment" is too all-encompasing to be considered as a single environment.
What if you change the initial conditions of the environment?
Then A would act differently, but B would still act the same because it is blind.
So now they are not taking the same actions. It seems impossible to have a blind agent that follows a non-blind in all situations.