From my understanding of the coupling through the lightning seconds mechanism as Dje described it, the following happens once you activate the chronograph: The cronograph train pushes the upper star forward and through the pin in the hole the pressure is transferred to the lower star and then to the escapement wheel which prevents the lightning second wheel from spinnig freely, but makes it advance with 1/6 sec. steps instead.
More pressure on the escapement wheel=greater amplitude. There are no miracles here. By adding the dedicated chronograph power train, JLC infact reversed the usual effect of the ballance amplitude drop with an increase.
Anyway, I don't think this a bad thing - the only thing I know about having too big amplitude is called "knocking", when the balance wheel actully hits the anchor when it's at the point when it's supposed to come to a stop before reversing its direction. But this requires amplitudes closer to 360 deg. Does anyone know of any other problems?
I'm pretty sure it shouldn't be a problem here, after all the lightning seconds wheel is very fast spinning one (once a second), meaning the force it applies to the escapement wheel should be very low comparing to the one induced by the fourth wheel of the main power train (which usually spins once a minute) ...