FWIW the electrical code (here) states that you need to have primary feed capable of full rated power of the VFD, so #8 it seems a bit silly but I think their rationale is that under certain fault conditions the VFD could continuously pull much higher current than the #12 would support. That's assuming the breaker would be capable of providing said current. In practical terms 3HP = 17A @240V full load, so #12 and a 20A breaker would support it. Another rule is branch circuit should not be loaded more than 80% of breaker so a 20A breaker and #12 copper will work but will violate the 80% rule. If it were me I would consider #10 especially if the breaker is any significant distance from the VFD. If you do use #12 copper make sure the breaker is 20A max.
If there was ever an electrical "issue" with insurance involved they may be looking for an excuse. I'm not up on the code state side, but I imagine the code is pretty similar.
Edit: Armoured cable may help somewhat with EMI. Keep the cable between the VFD and motor as short as possible that's the noisy cable with the sharp edges that will produce most of the electrical noise.