Please excuse the threadmancy...
I am pretty by the book for the most part..
But, here is your walk around all this pedantry for the sake of argument.
I am 5th level human alchemist I took Vestigial Arm twice at 2nd and 4th levels. Two-Weapon Fighting, Point-Blank Shot and Rapid Relaod feats at 1st and 3rd levels. I am using my Vestigial Arms to hold my crossbow and then reloading as a free action with my normal arms which I would be able to do anyway there for no extra actions. NOW they are not giving me any "extra" actions that I couldn't take without them. Here is why:
Round 1: Crossbows loaded shoot both. (Could do this anyway with TWF so no extra actions there. and the arms by RAW state they can attack for you.)
Free action to reload cross bow with my normal everyday arms that I already possessed from the get go. (And the other is not an extra action because I could have dropped the first if I wanted after loading it and then loaded the second as an additional free action then picked up the first as a move action. so there for no extra actions.)
Fire both Crossbows. (Still not no extra action as that is part of my already existing attack regiment.)
I can't see how this is not RAW.
He could do it with repeating light crossbows as it doesn't say you take a action to crank it you just use two hands.
That fact that you can preform a free action with it is beside the point really. Are you telling me that if I already have a poison in my Vestigial arm and a knife in each had I apply poison two one as a swift action and then fight TWF style you would not allow this because my extra am used a Swift action. Really? How is that different then I have it in my off hand apply, drop empty vial(free action), draw second knife (quick draw, free action) and do the same TWF attack actions. I am not asking for an extra move action or a standard action or even an attack I am asking to make life simple.
I personally would feel ashamed to do that to a player and would never play in a game with a GM like that. But hey, that's personal preference right.