Microstrip traces over ground plane makes a transmission line, a two-port element. Within the transmission line, the signal couples to the ground and vice versa. When the plane is the reference place, the coupling is trivial (there's no induced interference from that which is defined as zero). When the plane is a supply, there may be noise on it, relative to the actual reference plane, and some amount of that will be coupled into the signal trace.
Whether that's a problem, depends on the application, signaling and so on.
For a typical example, where the power plane is wide, closely coupled to the ground plane (e.g. bypass capacitors scattered around evenly), low ripple (a typical digital design might have 10s mV of ripple, if that), and LVCMOS digital signaling is in use, the signal level (3.3V say) so thoroughly exceeds the plane's ripple that it doesn't matter, and it's as good as ground for signal purposes.
The same might not be true of an analog signal, or RF.
Note that you can also do a pseudo 3-layer layout, i.e. preferring top routing where possible, and keeping bottom routes short (jumpers at bus crossings). This may take up more board area (forces a lower component density) so it depends.
Tim