My understanding is AFCI breakers look for the frequency associated with arcing, usually around 100khz.
How wide of a range around 100kHz, and for how long, and the magnitude, probably determines how sensitive they are and how much nuisance trips you get. This is probably why they can trip if there's other noise in the area at this frequency. (RFI?) Or if your also imposing a high frequency communication signal onto the 60 hertz circuit.
My understanding is fluorescent lighting is just arcing in a special gas between two electrodes, and a high impedance transformer (ballast) that limits the current so that this "short circuit" arcing doesn't trip your breaker, while also boosting the voltage so you get the arcing. Maybe this arcing frequency in the gas gets transposed into the current being drawn on the line side of the ballast and is detected by the AFCI. That is, typically the ballast should smooth the current being drawn, but if the arc is drawing current (in a: "now I am, now I'm not" fashion) at 100 kHz, the line side of the ballast and AFCI may see some of that too, and trip.
Regarding a kinked wire tripping them, as mentioned above, there was either some arcing occurring where the kink caused the insulation to be stressed. Or perhaps it caused a reflected wave back to the AFCI that it saw the interference pattern that mimicked 100khz? Doubtful though, as probably any wire termination (boundary) could have this.
:2cents: