Not only does the person's account need to be on the PS3, but if it is PS Plus content, then the PS Plus subscription must be valid (not expired) in order to access the content.
Any content that tells you that it can be used if you renew the license is useless to you (you must renew PS Plus on the account it was originally on, and if you are renewing PS Plus, you might as well get it on your account and get the content yourself instead of trying to play it from someone else's account).
If the content tells you that it is inaccessible, it is because the account it belongs to is not on the PS3. In order to put the account on the PS3, you must know the email and password of the PSN Account. If you do not know this, then this content also is useless to you.
Any content that is PURCHASED through the PSN, not free, can be accessed at anytime with any account, as long as the original account that purchased the content is on the PS3. If the account isn't on the PS3, then these games are useless to you as well.
To put it simple, if you can't access the content when you click on it, then it is useless to you (unless you know the PSN Account info the content belongs to), so you might as well delete it, as it is taking up valuable memory (don't forget to delete the Game Data also to gain memory back: XMB > Game > Game Data Utility > Game Data you want to delete > Triangle > Delete).