This amuses me too. We had to bootstrap from nothing originally too. I think many have never learned the history or started from first principals.
I doubt that the original Unix was written without an editor, using only cat. Of course some earlier interactive system at one point did have to come up without an interactive editor... but still I'd think it's much more likely that the editor was written off-line and fed into the system on punched cards or tape rather than cat'ed from the terminal.
The original post only mentions the network and implicitly the keyboard as possible inputs, but of course the challenge would be much easier if you allowed a DVD, CD, or even floppy drive with drivers (which are part of the kernel). I think pretty much any historical bootstrapping of an interactive OS is much closer to this setting.
For whatever it's worth, Wikipedia (https://en.wikipedia.org/wiki/History_of_Unix) says: "In about a month's time, in August 1969, Thompson had implemented a self-hosting operating system with an assembler, editor and shell, using a GECOS machine for bootstrapping." I'm sure there are more details to be had somewhere.