I'm not saying it's a perfect indicator, I'm saying it's a cheap and easy indicator. Certainly there are outliers in every direction, but a running back who runs a 5.0 forty just isn't going to be very good (unless he's like 400 pounds).
So is it more likely that Google is filled with idiots that can't see the err of their ways, or that, across tens of thousands of individual hires, this is the most cost effective and produces the best results (minimizing false positives) on average.
College-admissions style interviewing just doesn't make sense for a company like Google.
Google has separate tracks for FE SWEs as well. It's just that you also need a basic proficiency with C++/Java and algorithms to be a Google FE SWE, while I'm not sure that Facebook requires that? (Perhaps because Facebook's frontends are written in PHP instead of C++/Java.)
Actually, I'd say that whiteboard interviews are for Google are an arbitrary way of selecting from already qualified candidates, just as 40 times might aid a team in choosing between 2 otherwise similar players.
The players invited to the combine are the ones teams are considering drafting anyway; all the 40 times do is move players up or down the list by generally small amounts. The point isn't that 40 times are useless, it's that they provide very little additional information about a player. Champ Bailey was going to be a high draft pick no matter what he did at the combine, and everyone already knew that Trindon Holliday was fast but probably too small to succeed in the NFL.
Likewise, someone with a 3.9 from MIT or a bunch of good open source work who's coming for an in-person interview is already qualified, and the whiteboard doesn't tell you anything new. I'd guess Google sticks with them for the same reasons teams tout 40 times - it's good marketing both internally (making decisions seem less arbitrary) and externally (look how tough our interviews are is a more socially acceptable way of saying look how smart we are), and it allows people to deflect blame if a hire doesn't work out. Judging by the number of posts about Google interviews I see here and elsewhere, the marketing is certainly successful.
The vast majority of interviews do not result in a hire. (Some of my coworkers have reported giving 20 in a row without a single offer.)
Also, I think your view of the interview pool is somewhat skewed. Most of the candidates I see do not have 3.9s from MIT (BTW, I believe MIT has a 5-point GPA, so it really would be 4.9), and a lot didn't go to Ivy-League universities.