Here's the point where we seem to be running into confusion. When you say "the old rule," which rule do you mean? Can you quote the exact rule you are thinking of - no more, no less?
Here's the entire text of the rule
I'm thinking of. Let me know if it's the same as the one you're thinking of:
In their Shooting phase, units may choose to Run instead of firing.
That's it. That is the
only rule that Battle Focus countermands.
Dex trumps rulebook when, and only when, there is a conflict. That's what page 7 says. The
conflict is critical. The BRB says that you cannot run and shoot. The codex says that you can run and shoot. One or the other statements, as a matter of logic,
must be false. That is a conflict, plain as day.
Because there is a conflict, the BRB rule goes away and the codex rule takes its place.
But there is no conflict between Battle Focus and the other rule. The BRB says that you cannot run and assault. The codex says that you can run and shoot. As a matter of logic,
both statements can be true. There is no conflict there. Because both statements
can be true, the rules do not tell us to delete
either of them.
I think this assertion rests on an important assumption, so I want to try to draw it out. Why do you think that "Units that Run in the Shooting phase cannot charge in the following Assault phase" is
dependent upon "In their Shooting phase, units may choose to Run instead of firing?" Your approach seems to assume that those are not two independent rules. Why do you think that? Is it something in the formatting? Do you have a logical proof to present that one
must be dependent upon the other? They look like two completely independent rules to me.
If they
are two independent rules, then overriding one (i.e., In their Shooting phase, units may choose to Run
instead of firing") does not call into question the other (i.e., Units that Run in the Shooting phase cannot charge in the following Assault phase).
If they are independent, that would be like saying, "Look, the BRB clearly doesn't contemplate units being able to shoot and run in the same phase. So clearly, the rule that blast weapons cannot fire Snap Shots is now called into question." Your approach only works - in fact, implicitly assumes - that they are not two independent rules.
Why do you think that?