You and all of the above are correct.
There is no requirement for a CdP Carnet to enter a personally-owned vehicle into the Netherlands or any other EU country.
Here is the official Netherlands Customs website own statement in English:
Cars, motorbikes and trailers
"Cars, motorbikes and trailers
If you travel to the Netherlands by car, motorbike or with a trailer with a valid number plate of the country where you live you do not have to report your arrival to Customs. In this case, you may take your car, motorbike and/or trailer/caravan across the border and use it in the Netherlands without having to pay taxes.
If you are not a Dutch resident
If you are not a Dutch resident then you may use your car, motorbike, caravan or trailer in the Netherlands for a maximum period of 3 months without having to pay tax."
I think if you send and cite the above official Netherlands Customs website statement to your Amsterdam freight forwarder and NL Customs, that should be enough to clarify your situation.
It's not uncommon for seaport/ freight Customs (and freight forwarders) to assume that anything entering through a seaport or airport is business/ commercial goods, rather than "personally owned" [vehicles]; and, Netherlands Customs website does reference use of a Carnet for import of business goods....unless you are personally present to document that this vehicle is your personally-owned vehicle.
In other words, there may also be some confusion because you are not personally present with the bike in Amsterdam during the Customs import/ clearance process, to show your personal passport ID and vehicle ownership papers, but are having a freight forwarder do the import clearance on your behalf.
Get back to your Amsterdam freight forwarder, show him the NL website language and offer to send the freight forwarder any additional documents to prove the bike is a personally-owned vehicle.