I just got to the SKL and handed my boarding pass to the lady, it was scanned and I was admitted no problem to the F side.
After a few minutes one of the SQ lounge ladies I know from visiting SIN quite a bit came over and we had a chat. First, she wanted a picture with Bongo because she missed out last time.
Second, I asked her about UA pax being able to access the SKL. She said that if a Pax has a confirmed seat in either C of F, they can enter into the SKL in the appropriate lounge Business or First. Not an issue.
So my friends..there you have it...straight from SQ!!!