Not necessarily true - a few weeks back I noticed that I had no free space left on my iPhone. Applications were crawling, taking a lot longer to load and/or crashing, even after a reboot.
After removing a load of songs and pictures, things went back to normal.
Now, I doubt the Flash memory is used for virtual memory or ramdisk, but it seems like not having free space can cause problems with apps which are expecting to have access to local storage.