It's unclear the cause of this, one might infer it was US pressure to adhere to the agreement after finding non-compliance, alternatively it could be internally originated investigation.
Hmm, what makes you think that? I didn't see any indication in the article that the Chinese branch was not testing to the standards of US certification.
They were not. Not even "kind of". For them to be fake they'd need to be made out as something they are not[1]. The companies who acquired those certificates just weren't aware that certificates from that particular branch weren't permissible under SK rules - likely not even authorities in SK were aware until they had a closer look.
As an analogy, a driver's license from one country may not allow you to drive a car in another, but that doesn't mean it's a fake license.
[1] Edit: Some outlets claim there were fabricated test records, if that is true and not just journalists writing whatever, then they would be indeed fake.
IMO this is a somewhat grey area. Not familiar with regulations around testing labs, but om the surface looks like an innocent cost optimization that someone decided to put some pressure on.