There seems to be a change in functionality when you’re NOT connected to the internet. I have always been able to use a external hard drive connected to a router via USB and shared via SMB to my AppleTV (4) without internet access. It seems this functionality is no longer available.
I also was able to run a Speed Test within the Infuse Settings, where I was able to connect to the shared folders and video files to run the test. The test ran flawlessly without being connected to the Internet. This means the Infuse app is seeing my share properly.
I think this maybe a licensing issue. Where Infuse goes out to the internet for a moment and then runs the video. But without internet access there is no functionality in running a video on an AppleTV using Infuse.
NOTE: of course I access the Internet to sync the video metadata information to my AppleTV.