I wasn't taking the word streaming quite so literally. I assumed that you would be allowed to download these games to your hard drive, but you would be required to be online in order to play them.
Doesn't work like that because the PS4 hardware architecture is very different to prior Playstations and they can't play these games for technical reasons and not because Sony has included a special chip or patch that prevents it.
PS3 and older games will be processed on Sony servers and you will just receive the video feed that is calculated based on your controller actions. As i said the main problem will be stable connections and lag. May not be an issue if you play a game that's not decided in milliseconds such as adventure or roleplaying games (especially japanese Rpgs with their turn based combat system) where such lag may decide if you hit or you will get hit.
People with good connections may obviously get more out of PS Now, the rest may be hosed but do you want to fault Sony for that if you live in an area with mediocre or bad internet availability?