Geez everyone is acting historical over this but lets look at the facts;
1) Sony never advertised "PS2 Backwards Compatibility", people just assumed it was because Digital Foundry discovered that the games are using an emulator.
2) These PS2 games are being sold as PSN games for the PS4, they are essentially new PS4 games, just like all those other PS4 arcade games you can already buy which are also being emulated and have trophies.
3) Because 1 and 2, this explains why PS2 classics on the PS3 (which ARE part of the PS3 Backwards Compatibility including the digital copies) DO NOT cross over to the PS4, it's NOT the same type of games, one is part of "Backwards Compatibility" while the other is just a PS4 game which just so happens to work through emulation, alternatively it could of been a cheep dirty port but the end result would of been the same. In other words it's apples and oranges.
4) People hyped themselves when little info was known, now they are angry that they didn't get what they thought they would get despite "Backwards Compatibility" never being mentioned as a thing on PS4, at least not pertaining to current PS2 games on PS4.
As much as I would of loved this to be proper Backwards Compatibility like the xboxone, considering I have tons of PS2 games on hand, this was clearly not the case based on the facts at hand, but not all may be lost, their still could be hope!
The way I see it, there still could be an actual proper Emulator for Backwards Compatibility in the works, you see I believe that the current PS2 games and future ones will be used as part of a beta run for the PS2 emulator. Obviously the PS2 games out now will be refined as people start proving feedback on performance, this will help refine the emulator more and more, not only that by by the time the PS2 emulator has a solid performance on most PS2 games, say 50-80% of the PS2 library, the Trophy sets for PS2 games would have also built up for the most poplar games. So if I'm on the money, then Sony could announce an official Emulator for proper Disc based Backwards Compatibility at E32016 (including PS2 classics on PS3 being made available on PS4 as Sony merges the PS4 version of PS2 games and PS2 classics together), the caveat being that the emulator would be sold for say $30-$60.
I'm hoping that my theory is correct, at least this way if you want digital PS2 games you have an option, and for those who want to play their PS2 Discs on PS4 then we too would have an option even if we have to buy the emulator. I think it would be a win win, we would get 2 options to play PS2 games and Sony will get to make money on both the digital games as well as the emulator, after all the emulator ain't cheap or free to make so all things considered this would be the best possible outcome.
Anyways, just my 2 cents on the matter since everyone and their mother is gaming ape shit.