Jonathan Billings:

But seriously, was there something about these errors or other
effects that made you think it was something other than DNS being
broken?

Stephen Morris:

I would have thought that if my wifi connection had been temporarily
disconnected, hence the data couldn't be retrieved, I would have
gotten popups from fedora around the disconnect/reconnect.

You could get unable to resolve hostnames due to a networking problem
with your system, your router, your ISP, the route to the host, the
host itself...

But the messages showing that various different domain names couldn't
be resolved virtually discounts its being the end host (unless they all
happened to be on the same server, but I seriously doubt that).

There's every chance you struck a moment while your ISP was fiddling
with things, or something failed there.

I would have also thought that if it was a broken DNS the reissuing
the dnf check-upgrade would have repeated the messages.

I don't see anything regarding that in your log (you mentioned it, but
didn't show any logs).

With the reissuing of the command not producing any messages about
refreshing the repositories in question and saying there were updates
to put on, it had refreshed the repositories even though it got the
error, and there were actually no updates?

We can only guess that cached results were used.

Unfortunately you haven't shown us anything else to diagnose the
problem.  Such as using the dig tool on those and other addresses.  The
output of ifconfig, or other commands, showing the network parameters. 
Was there a gateway, a DNS server, did you get a real IP address?  Nor
did you tell us whether anything else was working at the same time (web
browsing, etc).