Chief Delphi - The Center Wheel

First step: Read the paper that Joe Ross linked to. It explains perfectly how the statics of a 4WD robot works. For a dropped-center 6WD, plug in Lwb = the distance between your center wheel and either outside wheel (so a 38 inch long 6WD wheelbase is effectively 18 inches long as opposed to 38 inches for 4WD). This shows why dropped center 6WD bots can spin on a dime, as Lwd > Ltw.

On how team 25 can turn without a dropped center wheel - there is no magic here. Just look at the math!

A robot with 3 wheels per side in contact with the ground is an example of a statically indeterminate system - we need to look beyond statics to figure out how much load is being supported by each wheel. Clearly, the more weight that is supported by the center wheel, the better you will turn (assuming your CoM is on or near the axis of the center wheel). By using information about chassis stiffness and the moments of mass distribution about the chassis, you could solve this problem to figure out just how much of the weight the center wheels are supporting vs. the outside wheels.
Assume that team 25's chassis is perfectly rigid and their mass is uniformly distributed. In this case, the 6WD closely resembles a tank tread system. You'll notice that in Chris Hibner's white paper, this very case is discussed! It turns out that for a tank tread, the effective Lwd is actually only 2/3 of the distance between the outside wheels. Of course, there IS no such thing as a perfectly stiff chassis, so the effective Lwd is going to have a bit of a fudge factor.
Assume team 25's actual wheelbase length is 32 inches (38 inches minus half a wheel diameter - approx. 4 inches - on each side). Assume their wheelbase width is 24 inches (28 inches minus half their tread - approx. 2 inches - on each side). 2/3 of 32 inches is 21.3 inches, which is less than 24 inches! So the Drive Train Basics white paper says that turning is possible.
The other piece of the puzzle is that team 25's wheels do not have the same traction in the X and Y axes. The siping pattern is designed to grip more in Y than in X (similar to wedgetop conveyor belting). Moreover, at least on their 2010 machine, there is a denser siping pattern (and therefore more grip) on their center wheels than on the outer ones.

So, the short version: Team 25 can turn because a non-drop center 6WD is still going to have a shorter effective wheelbase than a 4WD bot, and their wheels are grippier in the forward/back axis than left to right. Balancing these factors to effectively mix speed, maneuverability, stability, and pushing power is somewhat of a black art, which is why there is only one team 25.