Is it a gross generalization to say that if you're visiting a site whose name resolves to a private IP address, it's a part of the same organizational entity as your computer is?

The proposal here would consider that site local and thus allowed to talk to local. What are the implications? Your employer whose VPN you're on, or whose physical facility you're located in, can get some access to the LAN where you are.

In the case where you're a remote worker and the LAN is your private home, I bet that the employer already has the ability to scan your LAN anyway, since most employers who are allowing you onto their VPN do so only from computers they own, manage, and control completely.