The answer is a very simple one: There is a deep historical connection between the Jewish people, hotza'ah, and keeping the Shabbath. [see: a taste of shabbath]
When I wrote that post I said this:
Well, back then I'd never learned the opening mishnah of Masechet Shabbath. On learning that mishnah, it's now clear why Masechet Shabbath starts with this issue.
It seems to me the two stories are very connected, and it actually makes plain to us how thoroughly connected the mitzwah prohibiting tiltul (carrying without an eiruv) on Shabbath is. From this one simple Rabbinic enactment entire communities of Am Yisrael have grown to complete Shabbath observance.