A coco usually *wasn't* booted from a "dos" disk. The ROM-resident basic (the ROM was in the disk controller pak, a plastic box about the size of an 8-track tape that plugged into the cartridge slot on the side, where the black door is) contained a rudimentary set of disk management commands. BASIC versions varied from 1.0 to 1.2.

Maybe you're confusing two different sets of memories in your head. (The kid had a hacked with CoCo and you just don't really remember anything much about how it worked specifically. Honestly. .. the CoCo would not have made much of an impression on a kid with a c64. The 6809 in them is one of the best 8-bit CPUs of the era and it had a good BASIC, but the graphics and other features were frankly crummy compared to most of the competition. They're the sort of thing engineers and Ham Radio nuts appreciated.)