If the network is set to public then the firewall will block all of the Multiplicity ports and Multiplicity will not be able to communicate. This is by design as there are few reasons to be using Multiplicity when not on a trusted network so we only create rules for trusted networks.
As for why IT would believe it was required to mark a trusted network as public is something they would have to answer themselves, but it doesn't say much if they apparently don't trust their own network...
The network public/private/work setting is stored per network, so it isn't because people sometimes use laptops on other networks.
Unfortunately if the machine is locked down too much you may be unable to open up the firewall ports, but then I would have expected you also to be unable to install Multiplicity itself as that will require local admin permissions.
Your best bet may be to see if IT will setup firewall rules which let Multiplicity work (the details are available as to which ports to open) when on a public network. If not, and this directly impacts your work, I would suggest raising it with your manager as ultimately someone outranks IT.
