This is an excellent and educated response. Too often, guys seek carpet cleaning advice from auto detailing forums, when, in most cases they should probably be going over to reputable carpet cleaning forums to learn the basics. That's not to say that there isn't good advice on AG.
APC's are the worst thing you can do for carpet.
As previously mentioned, chemistry is involved in reguards to cleaning carpet and especially when removing stains effectively.
APC's are generally a high PH product so there is a whole spectrum of stains that not only can't be removed, but that can also be permanently set by the high ph product.
Once you understand why tannin stains can more easily be removed by ph neutral or slightly acidic products, you'll be on your way to removing stains like a champ.
The same things goes and chemistry also applies to things like water rings, red stains, protein stains, dirt and grease stains.
Learn the chemistry first and then select product.
Generic, all purpose cleaners and spotters are not for the true enthusiast or professional detailer.
Next you have to move on to more advanced things like (previously mentioned) acid rinses, film forming and crystalizing encapsulation products, speciality product that are combined with heat etc. Good luck!
Can you recommend any good forums?