With the right UPnP serving app you should be able to stream web video directly to the PS3 without needing a web browser. I've never needed to do so but I'm looking at replacements to Mediatomb right now and I know I've come across a couple that should do what you want with a minimum of fuss. Serviio was one. Mediatomb might be able to do it with some custom javascript but upstream is dead.
I'm currently trying ps3mediaserver, because I just need something that can serve up video files over the network in any format without needing to mess around in XML or write transcoding scripts. It was drop-in and go.