I’ve latest firmware and here is the answer. You may not like it so. Yes, you can stream, but…
1. You will need DLNA player.
2. Very few formats are supported. For example I’ve a few mkv files and it cannot play any of them, but LG web site claims it can. It also cannot play DivX. At least in either case I didn’t find any one that it can play.
3. As another user answered, it cannot pause or rewind anything that it streams.
4. I’ve last year model LG BD670 and it can play and pause all files that I gave to it. It also can find and stream from shared drive – no DLNA is needed.
5. The minor advantage of BP620 is in playing VOB files. Everything else close to disaster in comparison to BD670, which is not perfect either.