is this conceptually different?
Yes. Well, different from the Handheld Sync functionality.
An App on an iPhone that can play music from a Server, being also able to download a copy of the tracks, particularly using DLNA, is completely different to an application on a PC being able to push files to an iPhone. Only iTunes, and a few utilities, are able to do that as far as I know.
I don't use JRemote on iOS, so I don't know if it can download tracks to the iPhone itself. I know that capability is planned for the new JRemote2 for Android. Search the forum some more. There have been lots of discussions.
i.e.
https://yabb.jriver.com/interact/index.php/topic,121993.0.html is recent and implies JRemote can't download files for offline playback.
https://yabb.jriver.com/interact/index.php/topic,123445.0.htmlhttps://yabb.jriver.com/interact/index.php/topic,123299.0.htmlSo I guess this is a feature request, if you want offline playback.
But as I said earlier, you can connect to your MC Server from outside your network, for example in your car, and playback whatever content you want to. You just need to set up Port Forwarding of port 52199 to your MC Server in your router, make sure your MC Server is always turned on, and connect using the JRiver Access Key method. Again, lots of information in the forum.