the other person has to be online to play and needs to be request first if I recall which most likely will prohibit the other user going into offline mode while their library is being accessed.
oh wow :| it even says remote access on the 2nd paragraph of the main page and FAQ:
Family Sharing is enabled in one of two ways: You can either locally enable sharing in Account Settings, with Family Sharing & Devices, or remotely respond to a user’s Steam request to share your previously installed games via email.
It's badly worded, but people definitely misunderstand this part.
The only thing that can be done remotely is this:
I installed Bioshock Infinite on device A on my account. Some other family member/friend logs into his Steam account on device A and sees that Bioshock Infinite is installed on it, but can't play it since he doesn't own it himself. Now he can send me a request to remotely authorise the PC for family sharing and can play my games if I accept.
This is not supposed to be a PS3 style account sharing thing.
So Shambles was right, to share your library with anyone, you do need to give out your username and password at least once.
There's also this:
See a family member's installed game that you want to play? Send them a request to authorize the computer. Once authorized, the lender's library of Steam games become available for others on the machine to access, download and play.
I wonder how people think the requesting would work otherwise. I can click on any game that is out there and get a list of everybody on my FL that owns it (and installed it previously.. somewhere?) so I can spam them with share requests?