I just want to point out 2 things:
1.) We don't know who actually posted that "video". I have yet to see the name of the poser, let alone actual images of the gameplay to validate the video.
2.) The phrasing (if real) doesn't really make sense in the interpretation people are assigning it. If the PS2 games they are going to launch onto PSN are not PS2 Classics, nor actual BC -- then they aren't exactly BC and its pointless for them to put that disclaimer in there.
IF this is real - I wonder if they are going to launch an addon device that you can plug into the PS4 via a USB port. The device itself allows for hardware emulation of the older games.