As it is clearly stated in many participating economies' websites this rule of matching passport number, I think they are just doing their job. FYI.

From Australia: http://www.immi.gov.au/skilled/business/apec/
Card validity period
Cards are valid for multiple entry to participating economies for 3 years.
Please Note: If you obtain a new passport, you must obtain a new APEC Business Travel Card as these two documents are linked.

From Singapore: http://www3.ica.gov.sg/eABTC/faq/faq.html
Would I have to replace my ABTC if I replace my passport upon its expiry?
Yes. You would have to apply for a new card under the category of replacement due to change of particulars if there is a change in the Singapore passport number.

From PNG: http://www.immigration.gov.pg/apec.html
PNG citizen APEC Business Travel Card will be valid for two years in the initial instance but may NOT be issued for a period longer than the validity of the PNG passport. Once the initial cycle of cards is re-issued it is proposed that they will be valid for a period of three yeas, subject to passport validity, in keeping with the APEC Business Travel Card operating framework.