What do you mean by "competence" in a receiving office?
I'm going to cheat by guessing off the top of my head, while the resources are probably right at the links I already posted. Sorry, kinda busy today....
Not just anybody can file in any RO (receiving office) of the PCT. At least one inventor or the applicant (i.e., assignee/owner) has to either be a resident or a citizen of the RO country. So, if your client is a US corporation or has at least one US resident|citizen inventor, you can file in the US RO.
Suppose everybody is from somewhere else, e.g., Singapore. The US RO is not "competent" (or the applicants/inventors are not competent -- I think it's the former). So, the case can't be filed there. If Singapore has a PCT RO, they can file there. I say "they" because I assume you're registered in the US PTO and not in Singapore's patent office.
Let's suppose Singapore doesn't have a PCT RO. Then, they can file in the IB (International Bureau) in Geneva. Can you represent them? Probably not. They can only be represented by someone authorized to represent them in at least one country that would be competent if that country had a receiving office. So, suppose one of the inventors was a citizen of the UK. A UK (or perhaps even an EPO) practitioner could represent them in the IB, or even in the EPO or UK RO.
So, that's what I mean by "competence". The PCT really means "official authorization to represent others" -- not "knows what the heck they're doing."
As for not wanting protection in the US -- doesn't really matter. You file in the PCT in the US RO and you have a pending PCT application that can be entered in the national phase to any designated PCT contracting state (country).
Just don't expect your IPER before the 30 months. IPE (Chapter II) in the US is absolutely useless and not functioning, except to defer fees (of the national phase) and to preserve choice (by postponing the national phase deadline in a number of countries). The only way to get your Written Opinion in the US RO before the national phase (when it still might be reasonably useful) is to select EPO as your ISA and they'll include a draft WO with your ISR. Of course, it's written by a searcher, not an examiner, so it's mostly useless. But the US RO Officer usually just ratifies the thing as is -- no "heavy lifting" (as in a pencil) in the US RO.
I have no experience with Korea as the ISA -- have no idea if they produce a draft WO with the ISR. I have no idea if they're any good.
Regards.