Sometimes COS is more important than FF status
For those pax who are 1K and flying either F or C (on non-SQ *A carriers) ex-SIN, it looks like that it is always best to avoid showing the SKL lounge attendants your 1K card.
Always show just your *A F or C boarding pass and you should be admitted into the SKL without any problems.
Remember, you are being admitted to the SKL based on Class of Service and not FF status. Showing your 1K card may give the wrong impression that you are are Y passenger trying to gain access and they might redirect you to the premier lounge.