This is true, but the issue is that is dumb! You really should be able to unbox a toy on Christmas morning have it work without going out the Internet and connecting to some account.
Maybe not all the functionality can be there, but functions that don't naturally require network access should not require network access.
As it happens, my wife bought me a PS4 for Xmas -- a massive upgrade over my 15 year old original PS2. It came in the box with GTA5 (on disc), and a coupon for a free digital download of another game.
It's been a PITA that PSN has been offline. There are a lot of features and functions built into the system that rely on online functionality, including for some dumb reason accessing the built-in web browser. However, playing GTA5 hasn't been an issue -- I just popped the disc in, waited what felt like an eternity while it installed itself (it didn't give me a choice, and warned me it could take up to an hour), and I was off and playing. All without having been signed into PSN.
In essence, the system worked exactly as you described that it should. A single-player game on disc loaded and ran just fine while PSN has been offline. Not all the functionality was there, but the major function that doesn't require network access (playing GTA5 in this case) has worked flawlessly.