It's true. The compressor flow has to keep up with the tool.
Otherwise, you run less than ideal pressure, and the motor gets over-worked (running constantly).
This is how I killed my CH 7gal in no time.

I just picked up a Porter-Cable 1.8HP 15gal.
It does 5.7 SCFM @ 90psi and 8.0 @ 40.
Not quite as much as I was hoping for, but it seems there is no such thing as a "mid-grade" compressor. At least it's brand new, so I have a warranty!

I also stopped at Princess Auto yesterday to see what they had, and I ended up walking out with a 230 volt MIG welder