Sony added 4 more GB of RAM for games, not for the OS. It would mean that out of the new 4 GB, only one is for games. I really don't think they'd make that mistake.
I don't think this is the case. In fact, I think it makes far more sense for Sony to disproportionately allocate the 4GB of RAM that they added to the OS. Think about it from their point of view and what they know about their competition. The extra 4GB was obviously a direct response to competition from Microsoft, who had 8GB. The most logical allocation of RAM for Sony would be to match Microsoft's allocation ratio. They already knew that they would have graphical superiority with their faster GPU and higher memory bandwidth, so from a competitive standpoint it makes sense to equip the PS4 to compete with Microsoft on other levels that they are aiming to have an advantage on. Sure, they could have thrown it all to games, and you would see diminishing returns between 5GB and 7GB. There is more value in putting it towards the OS, because it allows them to compete in a whole other sector.