I think the intended meaning is that everyone is running on the same source code. Even if the source code contains modules that take set values according to runtime events and then become irreversible (or extremely difficult to alter), which leads to the same "program" doing vastly different things and having different capabilities.

Well, this can be made trivially true through a suitable choice of the line between "source code" and "set values". For example, define the laws of physics and basic biology to be the "source code" and let our DNA and upbringing be the "set values". I fail to see how this is interesting.