I could certainly be incorrect, but I do not believe the Sistine Chapel closes any earlier than the rest of the Museum. Hours are basically 9:00 to 6:00 (M-Sat), but you cannot enter the museum (buy a ticket) after 4:00. At 5:30 they will start to usher you out of the room you are in and not let you into another room. Maybe what you were reading was some adaptation of this.
I will say though (unless they changed the flow) that the normal route through the museum takes you through multiple galleries, winding up at the Sistine Chapel, then basically to the exit. So I would not push the Sistine Chapel until the very end of the day, you might not be allowed in.