I missed my connection to SQ flight in LAX in March, due to a delayed UA flight (weather problem). UA-SQ all in one PNR. It was quite late at night (>11pm), LAX airport was jammed, every counter had a long line. RCC was closed. I called 1K phone line, 1K phone agent said free hotel is not an official benefit of 1K, although sometimes 1K members will get it, but airport agent is the one to give you the free hotel, not 1K desk. I finally got to speak to an UA counter person, but was denied of the free hotel ( I told him what the 1k desk said).
My conclusion is that, free hotel can be had by 1K members, but it is not an official 1K policy. So it depends on your luck.