I too have been looking into Class D amps for a project. I find that there are three variations. The typical integrated type (all in a single IC package) use a single power supply voltage as you describe and are wired BTL or have a series capacitor coupled output. I thought the later went out in the 60's but its back in class D, primarily for automotive market, I think. The former, Balanced Transformer-Less, uses two outputs where each output sit at 1/2 the power supply voltage. (Is this dangerous?) The two outputs are driven out-of-phase producing double the AC peak to peak voltage to the speaker and theoretically four times the power for the given power supply voltage. Also very helpful for automotive or inexpensive amplifiers of 100 watts or more.
Then, finally there is the type which uses two power supplies (separate positive and negative power supplies like most analog amplifiers) for a ground referenced output. These often use external MOSFETs to produce a good power level in a "normal" way. I think most of the professional sound amps are this style.
So it all depends on which driver chips or power chips you use, and there are so many these days! Hope this helps.