Yes they can. But in my experience, at big organizations, the people using Google Analytics are not developers and will have no idea what weblogs are or how they could use them to determine the real browser statistics.
I'm a dev and I have no idea what weblogs have to do with this discussion. Quick search didn't do anything to clue me in either.
Which part is confusing? The browser sends lots of data to the server with each request. The server usually logs at least some of that data. Among other things, that data can be used to generate a subset of the data that is typically gathered by GA and other client-side analytics tools.