Korea can accept whatever certifications it wants. This is Korea refusing to accept the test results performed at the China offices of a US company.

"Korea only acknowledges test results from the US-based BACL through an agreement with the United States, and does not recognize tests by the organization’s Chinese offices, the ministry said."

The language is a bit misleading.

Korea acknowledges test results from dozens of domestic and foreign labs. Labs already certified by the US, Canada, or EU are covered by a blanket agreement with the respective jurisdictions, and BACL is one of them. This helps reduce friction when importing/exporting from/to these regions. But the blanket agreement doesn't cover China-based subsidiaries of US-based labs.

It's most likely much cheaper for companies to certify once for US+Korea than to have to do so separately for US and Korea. Given that Korea is a smaller nation it's a win for them in terms of imports.