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To answer your last question first, I'd "assume that actions of the players are within the rules rather than the other way around" except when the actions of the players are not within the rules. The player committed an infraction of the rules (false start) - not within the rules.
To answer your other question - once you get to the point in the game (or half) where one team is obviously trying to (or would benefit from being able to) either A) conserve time or B) consume time, then this (stopping or starting the clock by R) comes into play.
This is amazingly straightforward, and I really am surprised there's ANYone disagreeing here.
You do have a point in that the rulebook would probably benefit from a stricter wording that takes away any judgement on the part of the official. But in this particular case, I don't think it's even necessary to judge the intent of the player committing the false start. It's obvious that the team fouling gains a significant advantage from committing that foul if you decide to start the clock after the foul. This is specifically the kind of case where you'd not start the clock after the foul.
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