It is correct that some motors do not like "modified sine wave" power.
This is also true of some power supplies in other equipment.  Without
looking at the specific device, it is difficult to know if it will work
on a small cheap inverter.  The best way is to try it.  With a motor,
be sure to run it for a while and see if it overheats or makes any
unusual noise.

I have a backup power system in my house and have been surprised at
what does and doesn't work on a "modified sine wave".  I never had
a problem with my piano motors but I have a diesel heater that has just
a small control circuit that refuses to operate on anything less than
"pure sine wave" power.  I had to buy a 2.5 KVA pure sine wave UPS
which was not inexpensive.  When I bought the heater I was assured that
it would work on an inverter.  They said that just to sell the thing.

Fortunately, "true sine wave" inverters have become much less expensive
than just a few years ago.  If you only need to power a small motor,
the inverter can be very reasonable.  There is a wide range of quality
and cost, so shop around.

Best regards,
Spencer Chase
Garberville, California
http://www.spencerserolls.com/