My understanding is that, except for the 2010RX, the (older) RXs have a viscous center (differential Torsen-type). I take this as meaning that the center differential will allow some slip; however, as slip increases the viscosity of the liquid increases and the differential become less accepting of slip, thus 'forcing' the rear wheels to drive (push) the car in addition to the fronts. -- The 'axle' differentials (front and rear) are both 'regular' differentials, i.e. they allow slip and the wheels with more grip gets less power. -- It would thus appear that if both a front and a rear wheel have no grip, the RX would be unable to drive forward.
I would be really interested to read a post from someone who knows for sure ....???
first - a viscous coupling is what you described, but is definitely not the same thing as a TorSen center differential. A VC has clutch packs floating in a liquid that responds to heat. When there are speed differences between the front and rear axles, the clutch packs slip, making friction and the liquid heats up causing the clutch packs to grab one another, essentially trying to match the axle speed between front and rear. This is why on vehicles equipped with a VC it is crucial to keep your tires rotated and replace all 4 at once, otherwise the VC is constantly getting hot and will burn up in a few thousand miles. A TorSen unit is a gear driven mechanical unit as used in most Audi Quattros, and does not rely on a VCD. You are correct that the front and rear differentials are open, so either the left or right side could spin freely; however if the rear was spinning then the VC should have already sensed that the front was spinning to send that much torque to the rear in a front biased setup like the RX has. I suppose it's possible that the hill was steep enough and that the rear tire spinning had so little traction that the VC could not transfer enough torque to the front. VC's do not "lock" like a traditional 4X4, and depending on the design there will always be some degree of slip.
edit: After reading my own post, I'm wondering if the original poster ran different diameter tires on his vehicle at some point, which caused premature wear on the VC?