Obviously all sites have a right to control/filter content, but I wonder if there is some law that a giant site must abide by some stricter rules of equal participation ..
Facebook is in the right here. Lamebook is clearly an attempt to cash in on the Facebook name, trademark law does not permit that, trademark law is correct here. Merely being "the little guy" doesn't make you right or give you carte blanche to ignore whatever laws you want.
The submitted article, however, quotes a law professor who explicitly portrays this as a first amendment issue which doesn’t support your hypothesis that the first amendment only applies to the government in this case. I’m relatively certain that Facebook is free to block Lamebook on their own site all they want. Freedom of speech doesn’t come into play. I’m not so sure about that when it comes to the trademark.
Now, I think Facebook has the right to block whatever links they want to block on their own website. It's their website and they should do what they want that they feel is in their own self-interest.
Casting this as Lamebook doing something that violates Facebook's trademark is incorrect without any actual evidence that they are indeed violating Facebook's trademark.
Merely having a name that rhymes with Facebook isn't enough to call that a violation of Facebook's trademark.
I have evidence that Lamebook is violating Facebook's trademark. There's the name. There's the fact that their logo is clearly a Facebook hand, only reversed. There's the fact they're in the same basic industry and a realistic chance that Lamebook could be reasonably confused to be connected to Facebook by a normal person. I'm not sure what other evidence you're expecting, a signed affidavit from John Roberts?
The basic industry is the web? That is a stretch. Does that mean anything else is in the basic industry of "physical things"?
Facebook is in the industry of social networking, while Lamebook is a 'lolpics' site targeted at funny things FROM Facebook. It seems like they are clearly doing what Facebook says they are (attempting to piggyback on brand recognition), using satire as a hook to get away with it.
Whether they will succeed I think depends on Facebook's ability to show that this use will harm their name / confuse their customers, and that seems doubtful. In a similar instance, Toys `R' Us successfully forced Guns `R' Us to change names; the case was made that parents would think that Toys `R' Us had a chain of gun stores!
The law is not unfamiliar with your objection. In point of fact it has dealt with this question rather frequently. And no, your made up pathological case has no ground in the law, and no, I do not think the law would slice and dice Facebook and Lamebook into separate industries. Separate industries are, as the link says, things that can not possibly be confused for each other, like a tax service and a farming implement company, not "a web-based social network" and "a web site for satirizing social networks".
Taking your point to its logical conclusion, two companies always differ on some irrelevant dimension; the ability to find some trivial difference will not protect you. It's the usual thing I think we computer programmers tend to forget when arguing about law... you have to convince a judge you're not in the same industry. It's not a computer algorithm that can be gamed with a bit of pathological input and a loudly-yelled "TAKE THAT!", despite how it may sometimes appear.
Though your last paragraph entirely confuses me; you express doubt about the court case going in Facebook's favor, then cite an example that I think is actually sillier than the idea that Facebook might spin off a site or two?
I think the biggest concern is that the social network effect creates a barrier to entry (it is hard to create a competing network with the same value to users as Facebook's because the value of people's existing networks outweighs the value of benefits like freer speech or a better user interface for most people).
Many governments regulate anti-competitive and monopolistic behaviour, with the aim of opening up competition in markets and allowing greater participation that way.
In this case however, Lamebook isn't really a competitor.