As per confirmation with several Chinese Visa centers /embassies:

The local Chinese embassy will accept the vaccination certificates from a third country.
There is no exemption for the above policy; all applicants (including children) must be able to present valid vaccination certificates to apply for entry visas.
Note: applicants are still advised to double-check the exact policy for their specific location.

If the principal employee is already in China with a work/residence permit, only the dependent family members will apply for entry visas to join the employee in China, and they are advised to double-check the policy with their local Chinese embassy.

This summary was prepared using information obtained from the Embassy of the People’s Republic of China in Algeria, Australia, Belgium, Belarus, Brazil, Denmark, Finland, France, Gabon, Germany, Hong Kong, Indonesia, India, Ireland, Israel, Italy, Japan, Macau, Malta, Micronesia, Nigeria, Norway, Pakistan, Philippines, Serbia, Slovakia, Sri Lanka, South Korea, Spain, Switzerland, Thailand, Turkey, UAE, the U.S., the U.K. and Vietnam (Chinese and English written sources).