It sounds to me like the A600 was being "ram kicked" with the 3.x kickstart file then booted into OS 3.x off the hard drive. Commodore and later various other "Amiga" makers would make new operating system releases available for developer use that would read the new kickstart ROM into memory and write protect it, then reboot into the new OS.
A lot of Amiga software developers used this feature to test out new versions of the Amiga OS. The technique of how this is done changed over time (depending on what cpu and how much mmu function was in the machine).
Originally the Amiga 1000 didn't have a ROM based kickstart, it was loaded in via some firmware called the "writable control store" on the original A1000. Kickstarts got as big as 512K in size which took away extra memory with kickstart being loaded into and execute in RAM instead of rom, but the technique worked well and still does for software testing. Many users use it instead of installing a new ROM and opening their case.
The ROM upgrade became a big source of revenue to dealers and Commodore alike, so they nixed the idea of kickstart in RAM (and loading in Kickstart off a disk) because some of the computing press was worried about how stable the machine would look if they didn't have a rom versus an Atari ST for instance which needed much more in the way of rom upgrades that they never got...
You can still get software to kickstart an amiga from RAM on Aminet (Zkick Skick etc). You need to make sure you have legal access to the kickstart file itself and that maybe another issue..
