Yeah, I really don't think Netflix streaming is in the BDP-S560's future. It's too bad because it seems to be a decent player. If you wanted to hang onto it, you could pick up something like the Roku HD for Netflix streaming.
Otherwise, the LG BD390 and PS3 are good solutions. If you're not going to do much gaming though, the BD390 is probably the better choice. I'm a PS3 owner but I gotta admit that Blu-ray/DVD playback and network streaming is clunky at best. Not to mention, you need to pop in a special streaming disc if you want to do Netflix. The BD390 does it all... Netflix, CinemaNow, Youtube, Vudu, DLNA, etc. and its cheaper too.
"Blu-ray is just a bag of hurt." - Steve Jobs