Apple TV tries to use plain http for remote viewing of live channels. Doesn't provide session cookies either. As if it were on a local network. Recordings work fine.
I have an Apple TV 600 miles away from my home that streams live everyday. Works perfect on all sources.
The private networks in both places are different so Apple TV doesn't think the DVR could be local?
Apple TV also tries to discover HDHR devices when streaming remotely for purposes unknown 
Don’t know why you have a problem. My kids live in another state and they have two ATV and use them everyday to stream off the server in my house. We are not on the same ISP or using any kind of VPN, just regular internet. Connection is fine. They watch my local tv stations off my HDHR and stream TVE without issue.
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Works fine if you use the supported method for remote access.
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