Perhaps I am missing something, but unless someone is a genuine contact, I see no benefit in becoming a name in someone’s collection of ‘friends’ on Facebook or ‘contacts’ in LI. Nor do I request that contacts of my contacts become Facebook friends or LI contacts unless I know them and they know me.
I would rather protect the integrity of these social media and do a little to protect my own integrity and privacy at the same time.

I have many LinkedIn connections, gathered over around 3-3.5yrs of LinkedIn membership. Whilst I HAVE connected with a handful of relative strangers, this is very rare indeed. The majority of my connections are people I’ve met (probably 90%+), and if not met then spoken to on the phone extensively (5% – particularly those business contacts I’ve made who work overseas), or had some extended email contact with.

What I’ve really noticed is that as my connections have increased, so has the number of random punters looking to link with me. I guess one is a function of the other but, like you, I’m somewhat suspicious of their motives – particularly from people who call themselves things like “professional networker” or “visionary entrepreneur”. Honestly, what do these people actually DO?!