I've been mentally drafting a blog post on exactly this topic, so while that percolates in my mind I'll answer with: it totally
is a filtering problem.
For a small company whose culture is in flux and needs the right person, it's absolutely a matching problem. You need to find the right person for the job, period.
At the scale of a company like Google, however, it's absolutely a filtering problem. First off, we're large enough that most (perhaps not all) people talented enough to clear our interviews will (given enough persistence) find a place where they can be happy and contribute. We can get away with not worrying about the subtleties of matching and instead only focus on technical skills.
Second off, the number of applications rejected for every hire is staggering, simply because of how many people apply. These numbers are fantasy, but imagine if you had to choose one person out of a hundred applicants, and you actually had the means to interview every single one. You're going to pay this person a quarter of a million dollars a year and aim to keep them for half a decade or more. The economically rational thing to do is be picky as all hell, and this is exactly how Google and friends do it.