The information offered by CP and Palmer is designed so that new brewers can get a decent beer in the quickest amount of time possible. If a lot of new brewers were told "you're looking at 6-8 weeks minimum before you can drink it," they'll be turned off. But if you tell them "3 weeks start to finish," then their interested is piqued.
Beyond that, I've conducted my own experiments, and can tell you that from my experience, leaving brew in the primary -- on the cake -- for around 3 weeks has noticeable/tasteable advantages (ie: we're not talking armchair expert stuff, but practical benefits).
This is because after primary fermentation is complete, the yeast are still active (contrary to popular/assumed belief). They begin feeding on the waste products of fermentation, thus cleaning up after themselves and giving your brew a crisper and less muddied flavor profile.
That said, you're free to do whatever you want. You can take it out of the primary after two days, ten days, etc, but just because that works for you, doesn't make it right. Indeed, most people skip the secondary entirely for a standard brew. A longer primary time has more or less displaced the secondary for most styles save heavy barleywines (which require bulk aging) and dry-hopped brews (or others that require post-ferment additions). In other words, the secondary isn't so much a vessel for conditioning of your average brew as it is a tool to improve upon more complex/advanced examples. And even with those styles where a secondary is to be used, I always keep it in the primary for 3 weeks first.
Where the average brew is concerned, you're better served by keeping it in the primary for three weeks and bottling (ie: no secondary). It makes the whole process easier, and introduces fewer vectors for failure -- while also offering improvements over the standard 1-2-3 methodology.
Bear in mind that home brewing is a fairly new phenomena (30-40 years). Hell, you go back more than about 20 years and you'd have a hard time finding a microbrew pretty much anywhere. The point is, craft brewing is not an ancient art form, at least not as it's currently understood and practiced -- it's a new and developing arena where methods and philosophies are constantly being refined.
Case in point: the extended primary is a very new technique, but one that has seen widespread use and appeal because, guess what, it works!