Getting PS3 games to run on PS4 isn't impossible, it's just a very complicated process and would require a fair amount of work.
1st of all you have to deal with the core issues that the PPC in PS3 uses RISC assembly language and the SPEs use it's own custom assembly language which is called ISA.
The code that runs on both of those processors in PS3 would need to be re-written or recognized as X86 on PS4.
PS3's SPE code could be offloaded to PS4's GPU in Backwards Compatibility, leaving a substantial amount of overhead CPU available for any tasks that need to deal with PowerPC processes.
PS4's GPU is substantially more powerful than the RSX.
Overall Sony could very likely write an emulation environment, basically a virtual PS3 to run on PS4's SOC.
Emulation handled in this way isn't the only possibility, Sony could re-write each game that users request, place a patch on servers for users to download when they're connected to the internet, though this is likely the more time consuming possibility.
I don't see why The ICE Team or some other development team that is familiar with PS3 and PS4 hardware, OS and APIs in both systems couldn't make a truly virtual PS3 that can run on PS4, it all just depends on whether Sony wants to make this work or provide the resources to make it happen.
Backwards Compatibility doesn't get in the way of PS Now, because the whole idea of PSNow is to be used as a rental service for people that don't own all of the games in the PS3's library or even for people that never owned a PS3 in the first place.
BC could allow Sony to sell more PS3 games, if people want a superior experience then the remasters and remakes will also sell, so really it's all money for Sony.
As for my reaction, I'd be impressed that Sony were willing to put the resources into this, though it's not impossible despite what some claim about this.
