Actually it implies that the current does not follow the voltage. If you look at the voltage across the resistor, it is a sine wave. That is why you need a CT, which shows the current without these effects.
Bill
If you have a 'current shunt" and a current that is set by some outside conditions, which is the normal use of a current shunt (measuring current without significantly affecting the circuit), then the actual measurement is of the voltage on the shunt.
The voltage is a result of the current, and "by definition" the shunt resistance should be chosen to be so small as to not affect the current. So if the voltage across the resistor does not follow the current, the resistance must be changing, (or it's not the only path for the current). You would not expect the current to be changed unless the shunt were a poor choice resistance-wise, OR the shunt had a really gross effect occurring.
it seems that the errors in the test you mention must have been due to something about the shunt changing, presumably the effective resistance.
The case of a test with a voltage source applied to the shunt resistor seems to be different.... the resistor could change quite a bit and the voltage would not change, but of course the current would. So the true test would be a constant current source, with the voltage across the shunt read out as usual.
Not all the effects of a CT are "classically inductive".... there are a bunch of non-linear semi-resistive loading effects as well, especially at currents well below the expected load current range for the CT. What happens as the core is magnetized by the measured current can be somewhat anomalous vs the actual current. Only once the core is magnetized does the CT begin to read out correctly.
Not saying there is no effect.... just thinking about how any OTHER effects can be eliminated so just the effect under study can be isolated.
I need to do some experimentation.