ATF classifies any firearm fired by electrical signal as Class III. They want to know if the possessors also posses a tax stamp.
All the rest is drama for the masses.
stay safe.
I won't go so far as to say it's an urban legend, because there is some truth to this, but any electrical circuit, solenoid, or actuator that only fires one round per press of the switch by the ultimate human user is
fine. They're not exactly common, but there are electrical triggers out there for some high end target guns, and designs for 10/22 bullpups that are ATF approved, that use an electronic trigger to get around having to deal witht the mechanical drag of a long trigger linkage and transfer bar.
If it activates the trigger multiple times per single action by the person pressing the button or switch, even as something as simple as a cordless drill with a cam in it's chuck stuck in the trigger guard, then yes, it's an illegal post'86 FA.