First of all, virtually all satellites have elliptical orbits. So if a cloud of debris is created around one of these satellites, then it will intersect with more than just those objects at the provided altitude. Some of the satellites are rather elliptical, and those few satellites would no doubt spread the damage to other planes as well. The most elliptical objects are often those with the most potential for damage, spend boosters.
Secondly, the impact events are very energetic. The most well known satellite collision was the 2009 impact between two satellites. Debris from that event has threatened the ISS. In fact, there's a nice graph that shows the altitude of the various space junk from Wikipedia. It should be noted that this includes all debris, not just the debris from this event, although a significant portion of space debris came from this event. Note that the debris is spread out. This makes sense, as the two objects hit each other at a very high velocity, and thus can change their orbits quite dramatically (Although the point of impact must remain as an altitude to remain, unless some external force (Atmospheric drag, solar radiation, etc) changes it later).
The bottom line is, a single event seems unlikely to trigger Kessler Syndrome. It does seem quite likely though if the number of objects goes up, we could indeed have such an effect. Satellite collisions are very damaging, and steps should be taken to remove debris if possible, to prevent the problem from getting worse.