However, it is important that the amplifier be stable operating into varying impedance loads: an ideally stable amplifier will typically be able to deliver nearly twice its rated 8 Ohm wattage into 4 Ohms, and should again increase into 2 Ohms.
'Stable' means that the amp won't oscillate when presented with the load in question.
Atmasphere, perhaps I'm not seeing the same things you are?
Perhaps. Take a look at Fig 4 at the link you provided.