"The errors came at the exact same time" ...
is your server and Jess's server on the same physical network?
and do they both have the same top level domain ... like jessesserver.toplevel.domain ... and yours ericsserver.sametoplevel.samedomain
"they try to upload using the school network (wifi or hardline), it doesn't work"
But, your test at home using a students account ... different physical network and probably coming to your server via some 'front door' (PC or Mac) no issues.
There is one setting in Moodles for restricting to an IP range ... doubt that y'all would have that.
More info ... server platform is? Are either of you true server admins or are you only Moodle admins? Operating systems have firewalls. Your servers? Are your servers in an internal private IP network ... you can see such access by looking at Moodle server logs ... in the Moodle Admin UX. Last column .. shows IP address.
Have y'all checked with network services dept at school about any changes recently made to the network? Uhhh ... ask nicely, they are a sensitive bunch!
'spirit of sharing', Ken