As I get it, this is a separate thing from "moving" less than 50% of your allowed motion, correct?
I believe so. I am just applying the rules we use for moving to other maneuvers as well.
What I made sense of the rules in Arms Law was that a character was able to move up to half of his BMR and attack with 0 penalty. Is that correct?
I don't think so, and I think this is what is causing you to have questions.
On p. 8 of the red band edition of RM2 Arms Law (the one with the red band on the left side of the cover, and the characters fighting a golden or brass golem on the front), under the description of the 'Melee Phase', it does say 'All characters may make a melee attack except those who have used more than 50% of their activity for the round.' That is true, but that doesn't mean that characters who have moved can attack with no penalty. If you move forward to section 5.2, on Offensive Bonuses, and especially to table 8.2.7 (p. 15), you will see all the offensive bonus modifiers. Down near the bottom is '-(variable) | Moving (normally the % of possible movement equals the penalty'.
What this means is that
any % of movement you take reduces your OB by a corresponding amount. Move 25%, and your penalty is -25; move 50%, and your penalty is -50. Move 1% of your movement, and your penalty is -1.
Some of us have found these penalties to be excessive; they lead to a game where characters are penalized for moving only 1', and no one wants to move at all in combat. That is why for example Spectre houseruled this to say that characters in his RM2 game could move 10' and not incur any penalty. We've also discussed allowing players some free movement in RMu, or developing a new skill (Footwork) that would eliminate these penalties.