While that may be true with other stock head units, the non-entune stock head unit IS processing the bass BEFORE it gets to the aftermarket amp.
If you use some simple test tools, such as a few audio sweeps as well as straight frequency files, you can immediately tell that the head unit is processing the frequency cutoff as you turn the volume up. I don't have the stock deck in there now so I can't verify my old findings, but the last time I tested it (back in Feb or Mar), I believe the cutoff frequency for the rear channels were at 31hz (IIRC). At higher volumes though, that would move up a few hz (something like 37hz?) as no sound from the test files below that frequency would be sent to the amp from the head unit.
Do some simple testing with the stock deck, you'll find the same results if you just add on an amp and crossover. While I'm no audiophile, I've been an installer since 1984 and even owned a small car audio and alarm shop in Honolulu from '88 to '95. I haven't been in the business for quite some time now, but when I heard the system after installing the amp and LC2i, I knew right off that something was out of whack. I tried and tried to tune it as best as I could, and while it wasn't half bad (which is why I lived with it for the last 6 or so months), certain songs would absolutely annoy me and I'd be constantly screwin' with the bass knob for the LC2i just to balance the system.
Today is a completely different story now! Full sweeps from 10hz to 10khz produces a very lineal volume, bass is now evident as low as 12 or 13hz (although not very loud with one 8" sub, but I can hear the fluttering of the sub!) and no matter what volume I have it at, there is no cutoff low or high. This is still with stock speakers and just one Precision Audio amp, running 2 ohms mono at around 250 watts or so into one 8" Polk open air sub mounted in a 4th order box. I'm now happy with it, but I just wanted to give the OP a head's up on doing the same thing I did not too long ago...