In your example, your description cannot be technically correct, although I am not denying that it introduces a degree of instability that would not otherwise exist. Traction control does not, and cannot, apply the brakes. It also does not assume you are or are not in a spin, only that one wheel has lost grip. More advanced systems, e.g. ESC, do detect spin, but they do it with a yaw rate sensor, so it is directly measured, not assumed. The normal operation of traction control is to detect one of the drive wheels spinning faster than the other wheels, and when activated it reduces engine torque (through triggering fuel cut, ignition retard, and/or electronic throttle closure).
One of the things that OEMs found after integrating systems like traction control, stability control, ABS, etc. was that at the boundaries of slip/acceleration/yaw between the systems and normal operation, there were discontinuities in the vehicle dynamics. So, that if you were accelerating, and a drive wheel slipped, there would be a sudden, dramatic reduction in engine torque; or in the event of an impending spin, there would be a dramatic braking of the inside wheel, which could lead to an overcorrection.
Over the last 5 years, the OEMs have realised this, and they have been working very hard to smooth the discontinuities that these systems create. There are all sorts of marketing words for this, e.g. Toyota have "Vehicle dynamics integrated management". All this means is that the sensitivity and power of these systems has been carefully matched to the car and each other, to avoid sudden shocks.