It sounds like a network issue - I might expect this kind of behaviour to happen if (for example) the C:\Windows\System32\drivers\etc\hosts file was pointing the Clarity URL hostname to the wrong IP address, or something like that.
So check that the hostname resolves to the correct IP on both machines with ping/nslookup.
If it's not a local configuration fault (like a bad hosts entry) then you can also try flushing the dnscache service (ipconfig /flushdns) on their machine.