the scan of the sheet the lounge dragon in lhr uses shows status only as a way to enter the lounges.
if this were true, if finnair called the front cabin F like AA calls its front cabin on short flights i.e lax sfo then one would be able to get into the first lounge in lhr by flying finnair for a short flight?
you must use the lounge of the airline your ticket is on if your using COS to get in. if it is status, you can lounge hop.
hkg is an exception to this rule they will allow ba f pax into the f section of the wing, i am sure there are other exceptions but as far as i know its just hkg