The crux of the problem is "what is reasoning?" Of course it's easy enough to call the outputs "equivalent enough" and then use that to say the processes are therefore also "equivalent enough."

I'm not saying it's enough for the outputs to be "equivalent enough."

I am saying that if the outputs and inputs are equivalent, then that's enough to call it the same thing. It might be different internally, but that doesn't really matter for practical purposes.

I think one of the great lessons of our age will be that things being apparently equivalent, or in more applied terms "good enough," are not equal to equality.