SQ does have some issues with allocating mileage to UA, and it isn't only for cheap fares. I flew a one-way walk-up F fare back to SIN last month and tried to get it credited to UA for miles and get the PPS sectors - no dice. SQ miles only, nothing to UA, even after I walked down to the Paragon Center offices to get it fixed.

Usually this is the biggest problem with SQ flights going TO Singapore, as the Gate Agents, etc. aren't familiar with the UA miles/PPS points double play. Then the robot action begins when you try to remedy the situation after the fact. Annoying but true.