what they are telling you makes no sense.

Well I'm not so sure.
Here is a similar personal experince.

I installed a 2HP Teco VFD on a rockwell 11x25 lathe with a 1HP rockwell
motor. This lathe also had a mechanical variable speed drive.
With the stock motor it would not start if the mechanical VS
was set above 800RPM. The motor simply did not have enough torque
to overcome the drag and inertia of the VS drive and spindle.
I changed some parameters in the VFD to increase the starting torque
and made it work pretty well. The caveat is that the motor would
probably burn out if operated at low speed with the amount
of low RPM torque boost I programmed in.

I have sense changed the motor to a 2HP Leeson inverter duty motor
and it runs extreamly well without any torque boost. I also
replaced all bearings on both jackshafts because they were dry.
This may have been part of the original problem.

I now have two leeson inverter duty motors and I believe they
are an excellent value. I paid 150 for a 2HP inverter duty
motor from an on line supplier. electric motor warehouse
or something like that.

chuck