Can I use the wrong end of a voltage regulator?
Most positive regulators can only source current, not sink it, so what you suggest would only work if the current being drawn from the 12V to ground was more than the 3.3V circuit. If it was not then the 12V output would rise towards the 15V rail and your 12V circuit would experience overvoltage, and the 3V circuit would not get enough voltage.  

The same thing would happen in reverse if you tried to use a -3V negative regulator hung off the 15V input. It would work provided the 3V load was ALWAYS greater than the 12V load, otherwise the 3V load would see overvoltage and the 12V load would not get enough. 

Usually when multiple voltages are required you want the grounds to be common so this seldom comes up.