Can a measuring instrument be a control variable?

When I asked for the control variables in this experiment to be listed, several people said "same voltmeter; same ammeter". I've been struggling for years to come up with words to explain why the measuring instruments are not a control variable. Today it came to me. With any true control variable, if you shift it to a different value, you change the reading for the dependent variable. With a measuring instrument, the idea is that if you change it to a different model, you should get the same reading. The choice of instrument should not affect the reading and therefore the measuring instrument is not a control variable. In the case of the ammeter and voltmeter, there might be an exception. It would depend on the resistance of the ammeter or voltmeter. In theory, a perfect ammeter has no resistance and a perfect voltmeter has infinite resistance. If this were not to be the case in a replacement instrument, then the readings would change. However, it would have to be the resistance of the instrument that was listed as a control variable.