Nonzero current at voltage zero-crossing when consuming reactive power
The voltage across an inductor, V equals the indutance x the rate of change of current passing through the inductor. In short: -

$$V = L\dfrac{di}{dt}$$

So, if the rate of change of current through the inductor is zero then the voltage across its terminals is also zero BUT this doesn't mean that there isn't a value of current present and that it has reached a peak like this: -



Picture source.