"If you look at HOW an inductor works, the current flowing in one
terminal ALWAYS equals the current flowing out the other terminal."

I think that is true. If you define current as electron flow, then the fields
and radiation that a large coil may be subjected to, will not increase or
decrease the number of electrons that the coil contains. As such, the amount
of electrons entering the base of the coil, will equal the same number exiting
the coil, with time displacement.
Consider a large physically long capcitor, with multiple plates. One can use
this as a loading element. There is no electron flow between plates. However
there is "displacement" current between the plates that has no physical
meaning. Now what? The capacitor will be just affected as a coil.
So, from the conservation of electron flow I don't know what to believe.

73 Gary N4AST