Since when do you need a license to modify something for your own personal use? If they've given me access to the source, I can just start editing to my heart's content...

Practically, yes, but legally, you may not have the rights to.

That's why it's explicitly listed as part of Freedom 1 of the four freedoms of software: https://www.gnu.org/philosophy/free-sw.html

DVD players.

I can't think of a single use case where I would want to hack on a 32 year old OS without distributing it.

Not quite the same, but it may be good enough for you: I guess you can distribute a patch, combined with a URL to the original download.