A typical VC would have the amp input on the left and the speaker on the right. Moving the slider up and down taps a different portion of the transformer. The primary (amp side) has a voltage to turns ratio based on how high the amp is turned up. The secondary (speaker side) just grabs a certain number of turns and based on the same voltage to turns ratio, has a fractional portion of the maximum volume fed out to the speaker.
This supports your "short" with the volume control at minimum. Short for the speaker, not for the amp. Turn it up one notch and it's not necessarily "high impedance" as you say, in the sense that the impedance slowly drops as you turn it up. It's only taking a fraction of the available level and passing it along.
Now my question to you was on impedance matching VCs which I have never used or looked into. I went to a client's house that had them and due to quality or some other issue, the amp was shutting down with four of these in circuit. I don't know who wired them or their quality and it's been so long I don't even remember what I did to fix them - maybe changed the taps?
They say two things begin to leave you as you get older. The mind, and...what was the other one?
