There are some features within Dynamics 365 for Finance and Operations on-premise which rely on an internet connection.
This means that the on-premise version DOES by default have a dependency on some cloud services - BUT you can turn that off, so there is no dependency.
As an example, last week there was an AAD outage, which affected on-premise customer's ability to log into the application. What was happening was - you'd log in as normal - see the home page for a moment, then it would redirect to the AAD login page, which was down, so the user would be stuck.
In the background this relates to the Skype presence feature - after the user logs in, in the background the system is contacting the Skype service online - which is what triggers that redirect to AAD when AAD is unavailable.
There is a hotfix available which allows a System Administrator to turn off all cloud/internet related functions in the on-prem version, details are available here:
Disable internet connectivity