Not true in my experience, if you paid for a 'F' award ticket.
A few days back, when travelling on a 'F' award ticket using DL miles, one of the segments (NRT-LAX) was booked in business class. Upon check-in at NRT, I asked if seats were available in first class and also mentioned that I had a first class ticket. The JAL agent who was handling the check-in took one look at the fare basis, passed my ticket to a SQ agent at an adjacent desk and about a minute later after some typing by the SQ agent, I was issued a 'F' boarding pass by the JAL agent. It was that simple.
Based on an conversation I had with an SQ check-in agent at LAX about a year ago, this is normal procedure. However, only the station that the flight departs from can make the change.
This isn't viewed as an upgrade. They are simply releasing a revenue seat they don't expect to sell a couple of hours before the flight to a passenger who is holding a 'F' award ticket.
However, since there are no guarantees -- Good Luck!