For local shops:
If any shop is not listed on the list and they parallel import their stock, warranty will not be valid.
If shop not listed on the list, and they take stock from from other shops who are authorized dealers, warranty will still be valid.
As for international sets, only sets accompanied by official sales receipts from authorized dealers are recognized by most service centers here in Singapore. This is true especially for most brands, Nikon included. How Olympus will handle it, is best answered by Olympus Singapore.
Ability to register your serial number in the website is no guarantee that warranty service is guaranteed. That is the same for Sony and Nikon warranty registration websites. In the end, they can still ask you to produce a proper receipt and warranty card before giving your warranty service. How Olympus handles this is best answered by Olympus Singapore.
Trying to win arguments here will win yourself zero points. In the end, it is the service center's prerogative to give you warranty service or not. Not us. Bang table also no use. So every time you buy from overseas, it is a risk you have to take.