For rectifiers, the easiest way to think of it is: No one wire on the regulator/rectifier can ever share a path with another wire. You can think of the chassis as one big wire, and you have to "float" the other three wires, however possible. Obviously, the "cheapest" way is to float the AC at the stator, as this requires the least amount of wire(two couple-feet long wires to the rectifier, one 10+feet long DC wire to the accessories.)
Also, diodes will fail to behave as expected at higher frequency AC, and it is even possible to ruin slow/cheap diodes/LEDs with high frequency AC.
(Long boring explanation below)
As you rev your engine, you are increasing the frequency of the AC generated. Diodes have a reverse recovery time, where they behave as nearly short circuits for a short period while voltage is presented in the reverse direction across them. This isn't an issue at lower frequencies, as the amount of time the diode spends in this reverse recovery time is much less than the amount of time it takes for the AC signal to swing deep into the reverse polarity stage. At high frequencies, the time the diode spends in recovery time could equal or be greater than the time the AC signal spends in reverse polarity. This means that the diode has to pass whatever forward current it was designed for, and now is also passing extra (possibly large) current in the reverse direction that all adds to the amount of heat the thing has to dissipate.
Luckily, in the case of a cheapo light bar, your LEDs are most likely in series with a high value resistor, which is probably why your bar still works after a cooling down period instead of being a bad paperweight.
Most likely, the Banshee's system is producing a lower frequency AC than the 250r. That, or your buddy got slightly better spec LEDs in his tail light.
TLDR: Rectify your AC with the right tools for the job!
