According to NeoGAF user “Bastion”, games purchased through PSN are playable for free on PlayStation Now. He pointed out that on the PS3 version of PlayStation Now, the games he already bought (Stick It To The Man and Saints Row 2) and are available in the current phase of the Beta are showing up in PlayStation Now with a cart symbol next to them, meaning the games had already been paid for.
The only thing that has changed is the wording when selecting the game. Clicking on it brings up the normal rental fee/rental period. But the fact that PS Now knows what games you own means they are working on something.
Bastion further went onto state that his PSN games were not available to play for free on the PS4 version, which could be the case of the PS3 app being more up-to-date as the console was the first device to receive the PlayStation Now beta.