They are sort of right but have implemented it terribly. Serving out a static webpage is pretty low on the "things that are exploitable" but it's still an entry point into the network (unless this is all internal then this gets a bit silly). What you need to do is get IT to set up a proxy and run apt/certbot through that proxy. It defends against some basic reverse shell techniques and gives you better control over the webhosts traffic. Even better would be to put a WAP and a basic load balancer in front of the webhost, AND proxy external communications.

Blocking updates/security services is dogshit though and usually is done by people that are a bit slow on the uptake. Basically they have completely missed the point of blocking external comms and created a way more massive risk in the process... They either need to politely corrected or shamed mercilessly if that doesn't work.

Good luck though! I'm just glad I'm not the one that has to deal with it.