Sounds like you are prettty close in your assesment.
A BTL amp puts out 4 times the power of a single ended. When loaded with a static impedance, you put twice the voltage you get twice the current, which means quadruple.
Most likely they are feeding the woofers in paralell through a crossover. Because 90% of the time bass is in phase and mixed equally into both stereo channels this can work.
Used to be there was one way to design an amp, well, I take that back. If you are interested in weirdo amp designs search this group for "single transformer stereo amp", something like that. I got in it, but the schematic is not supplied. Someone did email it to me though. Kinda anteresting, and tubes no less.
If you like wierdo amp designs, also check out class G and class D amps.
If you like all that, one of these days I am going to sit down and design a class D power amp that uses only one output device. I have the concept, and I am sure I can do it in the analog domain, but it is not easy. Also, if I want it to cover the full range for audio, it is going to be a very very fast four quadrant triac. I don't know if they make them fast enough yet, but that doesn't mean the circuit can't be designed, it just can't be built.
If I can get one that I can accurately PWN at like 60Khz or so, it is feasible. Otherwise it might make a good low frequency amp. Of course such a thing might already exist, I can't say that something does not exist.