Aeroncaman, you are completely correct that if you have the appropriate visa already (eg. a B1 visa) , you do not need the ESTA approval. If however you are going into the US by commercial carrier on the Visa waiver programme (i.e. NOT as operating crew) with only a C1/D visa (not appropriate for travelling as a pax) then as I read it, you will require an ESTA approval.
PL