Well, we mustn't critique the dead, now. I mean, it's not like some flight student somewhere could actually learn anything from that, right?
/end sarcasm
That analysis of the JFK Jr. crash is largely correct, but let me clear up a couple misunderstandings. First, he was not an instrument-rated pilot. He was taking instrument training but hadn't taken the test for the rating yet when he died. He was flying a Piper Saratoga, which is a very nice, very high-performance airplane, but it is a single-engine.
His crash resulted from a classic mistake that all pilots are warned against from their earliest training called "VFR into IMC". Essentially this means that he was trying to fly the airplane by reference to the horizon outside, but flew into a situation where there wasn't a visible horizon. This wasn't illegal, since he wasn't in clouds where a pilot is required (by the FAA and by reality) to fly by reference to his flight instruments, but at night over fog and over water the horizon may not be visible.
For aerodynamic reasons I won't get into here, virtually all airplanes are unstable about the roll axis. This means that if you have an airplane flying straight and level, and take your hands off the controls, the wings will bank in one direction or the other. Also for aerodynamic reasons, once that bank has started it will become steeper, and because the wings are turning as well as lifting the airplane will begin to descend. The turn and descent will both increase, entering what's known as a spiral dive, unless the pilot takes corrective action.
With VFR into IMC, the pilot loses reference to the outside horizon. If he doesn't immediately start using his flight instruments to control the airplane, he won't be able to keep the wings level. The abovementioned spiral dive will begin, and that dive is a situation that rapidly worsens, quickly accelerating the aircraft to beyond its maximum speed. If the pilot doesn't immediately recognize the problem and use his flight instruments to correct it, one of two things will happen, depending on how high the airplane was when it entered the spiral dive: either the airplane will hit the ground out of control at a high speed and steep angle, or the airplane will accelerate beyond its maximum design speed, at which point the pilot (who is now probably quite panicked) will make an abrupt control movement that will tear the airplane apart in midair. Either way the result is an unsurvivable crash.
It's likely that JFK Jr. could have told you all of the above the day before he died (as should have any qualified pilot). There are a number of reasons why he may have lost control the way he did. He had relatively little flight time (about 350 hours), and over half of that was with an instructor on board. That's well over the amount of instruction time he would have needed to reach his level of proficiency, and while more instruction is always a good thing, it may have indicated that he wasn't entirely comfortable flying without the instructor. Also, the Piper Saratoga is a high-performance, complex airplane. I don't know how much time he had in it, but he may have been somewhat overwhelmed by how much more advanced it is than a typical training airplane. This theory may be supported by the fact that the airplane had an autopilot. When he lost the horizon, he could have turned on the autopilot to keep the wings level, but he never did, indicating he may have been unfamiliar with the system.
Finally, he was apparently under pressure from his wife and sister-in-law to get where they were going, even after their flight had been delayed until night. "Get-there-itis", or pressing on with a flight that it's not wise to make, is a common killer of pilots; it's almost certain that had he waited until the next morning he would have made an uneventful flight. As it was, he became distracted or didn't notice that he could no longer fly by reference to the outside horion and didn't recognize or try to correct the problem until too late. Even non-instrument-rated pilots are trained to fly straight and level on instruments, and to make a 180-degree turn to get out of bad conditions, but night, complaining passengers, unfamiliarity with the aircraft, nervousness about not having an instructor, and/or all of the above contributed to his not recognizing the problem or not being able to correct it before it was too late.
It was of course a tragedy that three people died, but sadly pilots die every week by making the "VFR-into-IMC" mistake. The JFK Jr. crash was almost a stereotype of bad decision-making that despite all efforts to the contrary pilots still make far too often.
The loss of the young man who ditched into Lake Michigan wasn't exactly the same situation, as he apparently exhibited excellent piloting skills. His mistake was made hours earlier, when he chose to fly beyond gliding distance of land without flotation and survival equipment, and apparently miscalculated (or didn't calculate) his fuel requirements. It's a sad fact that the vast majority of general aviation accidents could have been prevented by proper planning or decision-making (including the decision not to go) before the plane leaves the ground.