Not to delve too deeply into semantics, but it sounds like the lionshare of the thread is directed at a question of groove and blues rather than rhythm. Rhythm is just working within a set frame of time and subscribing a set of instruments to that rigor.
As Basstrap said earlier, Radiohead works in quite complicated signatures, and the syncopation that is required across those five musicians is ridiculous. On the surface, it may appear that they don't have the most sensual of grooves, but the rhythm in their basslines and the precision of their percussion section creates a different order of rhythm... one that can be just as appealing as some of the overt examples.
Do the low frequencies necessarily need to be amplified in order for that aesthetic of rhythm to exist? I don't know. Why work in a convention that imparts a formula if there's a more interesting way to achieve a rhythmic sensibility?
In my opinion, it's often the death of a band when they try to "re-discover their musical roots"... Some are successful as they expand upon the sound and the vibe, but others stagnate in attempts to emulate.
Yes. I figure I'm entitled to a Don King moment or three.