The answer is simple: they are unfiltered extreme designs
To clarify: every solid state amp devoid of any input and output stabilization filtration stands a good chance of oscillation, assuming they are of wide enough bandwidth; this is why just about all of them feature input chokes and output inductors. But some manufacturers elect to put those filters outside the chassis, either in networks along the cables and/or in the inherent inductance of the wire itself. There are good reasons for having those filters outside the chassis, like moving the magnetic fields inevitably generated away from the sensitive circuit board. It is an extreme design approach, but when one is engineering driven - like Spectral - you do extreme things. In addition, I feel Spectral has selected cables with extreme linearity to mirror their own designs. This is all part of a "system approach", which doesn't really appeal to everyone - but there is fundamentally nothing wrong with this approach, from an absolute engineering perspective. To go to more extremes, you can imagine that the inductance required to stabilize an amplifier and still provide bandwidth out to MHz may be split between the inductance of a network box and the wire itself, meaning, you can keep the inductance constant for varying lengths of cable purchased.
I have posted the following before, it is taken from the Spectral DMA-300RS web page
http://www.spectralaudio.com/DMA300/DMA300.htm and it's referring to the subject of input/output filtration and how the internal wiring (never mind external) is designed to replace that:
This is an example of extreme engineering.
The truth is that, before MIT came into the picture, you will find older Spectral amps from the 80's that do in fact feature input chokes and output inductors, like the DMA-80 and others from the 1980's - and in those designs which did not require specific cables, you will find the output inductors mounted at the speaker terminals - a small optimization because the magnetic fields are away from the circuit board, but close to the speaker wires. Trade offs and optimizations, like everywhere else in this hobby.
Regarding the sound, I would not agree with KeithR even on older Spectral designs. The Halcros were and remain exceptionally dry, and the very bad definition of solid state (BTW, google images of Halcro amps to see those big-ass output inductors over the boards). The Spectrals and other high speed designs do face challenges not found in more conventional amplifier designs; thermal tails (memory effects) is one of them, which are more evident as the speed increases. The big leap in the DMA-300 and 400s and 30SV is the elimination of these distortions, and I know of no other high-speed designs that make such claims. To solve these problems, from what we are reading, they have gone (as always) to extremes, building custom amplification devices, and in the case of the output transistors, to using video devices of extreme bandwidth. There is no doubt that every generation of product improved upon the previous, and the exuberance we are now expressing is only referring to these latest designs. Personally, I have always said that I have the greatest respect for the tube device for its extreme linearity, and that I like Spectral for attempting to achieve tube behavior and performance in solid state designs without the tubes' shortcomings; the road has been long, but I feel they finally solved the problem.
The proof is obviously always in the listening, and if you were to listen to the 30SV->300/400 system with MIT cabling, you just maybe stunned. The problem in such aural evaluations is to find a system with equally worthy sources and speakers and room. I've been upgrading and modifying my components around them obviously in order to get the best out of them. On the other hand, you may not like the sound at all, and that's OK. I've heard people claim many times that Spectral (and others) is analytical - well, I'd say it's because the recording contains all of that information. Frankly, the best of tubes that I have heard are analytical too, and I just love that. Others yet will claim they like their Spectrals without MIT cables - all the power to them. However, it's probably no coincidence that Spectral owners on this forum are gaga over the latest offerings...