Confusion about primary ps4?

Just wanting to clear something up as I'm a tad confused, if I purchase a game on my account from my friends ps4 that I have activated as the primary, both me on my own console would be able to play it as well as my friend on his console? is this correct?

Ps, would that also work if I downloaded the game on my console first even thought my friends is set as my primary?

Thanks.

Setting your account as a Primary account it means that you and everyone else's account on that 'Primary' PS4 can access your games, DLC and so on.

If your account is only a secondary account on the console (because it's Primary on another unit) it means your games, DLC and so on can only be accessed when YOU are logged into that system.

Basically, any user on the system can use the content in the former, and only the purchaser of the content can use it in the latter. You can download it on any console first.

However your account can only be logged online on a single system at a time.If you are online on one system and log into another you will be logged out of one of the systems. So you can't use the primary/secondary system to get two copies of a single purchase then go online to play multiplayer against your friend.

If you purchase a game on your account it doesn't matter what's primary or what isn't. You bought it, you're logged in, it's yours.

Wrong.

Actually, the primary account can access the games offline.

The secondary account needs to have an internet connection. That's a huge distinction for those with limited internet connections.
I have two PS4s, so I make sure my main PS4 can go offline to play my games if my woman wants to play PS4 games in a different room. She needs to be online to access the content though.

What? Wrong? So if I log into any PS4 on my account I can't access my library? Go try it silly.