Cargo has an --offline option. It's actually pretty possible to use rust totally offline - the doccumentation can be built, for instance, then locally served with (iirc) cargo doc.
I recently realized I was the only person running the API locally when suddenly all our unmocked tests started failing only on my machine.
All other tests, including the ones on the CI server, were connecting to the hosted integration environment for any unmocked call (and thus randomly modifying state there).
I build and host documentation on every commit anyways in the CI. And yes, that is true, I eventually figured it out (had some issues with it at first) but it seems like GitHub is back up so all's well anyhow. I do however wish that there was some public mirror that cargo could fall back to, wouldn't that make a lot of sense?