If you read up you will find that a breaking wave has the power to capsize any boat if the wave is big enough, especially if that wave hits the boat side-on (basically no boat or ship is immune to this danger given a big enough breaking wave). The size of side-on wave needed to capsize a kayak is very small indeed - as some of us (me included) have found out when we have succeeded in executing this embarrassing manouvre when arriving back at a beach full of surf bunnies
One key to avoiding capsizing in breaking waves is to stay perpendicular to the waves. This can be difficult if you allow a wave to surf you in because, when a boat is surfing, if you allow the boat to move marginally out of a perfectly perpendicular course, then the rudder does not have the necessary surface area & power to counteract the forces pushing on the much larger area of the hull and forcing it to one side or the other... in which case the sequence will almost inevitably be: surf, slew, flip in rapid succession.
On the couple of occasions that I have managed to avoid the almost-inevitable 'flip' stage I allowed a wave to surf me in, slewed, so the boat was side-on to the waves, and the small collapsed wave then pushed me into shore with the boiling water of the wave right on the side of the boat and the boat almost floating sideways over the flat water in front of the wave (i.e the wave pushing the boat sideways and the boat side-slipping over the flat water which was visibly traveling under the boat as I was making my way to shore sideways on).
Since I never come in to shore in waves of any size without first removing and securing the mirage drive I can be pretty sure that the boat was able to side-slip over the waves because the mirage drive fins were not present to provide additional lateral resistance. Had the drive been in and the fins down I firmly believe that these waves would have flipped me in an instant, not necessarily due to the wave alone, but with the water passing under the boat at the speed of travel in to shore, if the fins had been in and down then the water exerting lateral pressure on the fins underneath the boat, combined with the wave pushing on the side of the boat above the waterline would undoubtedly have flipped me.
Relating this experience to getting side-on to a current in a river: if you are side-on in a current and not traveling at the same speed as the current and you have your mirage drive fins down, then the effect would be more or less the same as my experience - in other words current pushing the fins out from under the boat (to flip you upstream) or pushing the boat downstream over the fins with the fins catching in the water (to flip you downstream). I once saw a similar thing while kayaking down the Ardeche river in France years ago - the river passes through a gorge with near-vertical sides. At a bend in the river where the current had undercut the rock wall and therefore flowed directly into (under) the cliff edge, people whose kayaks hit the wall side-on were instantly flipped upstream. What was happening was that their boats hit against the wall which was then pressing on the side of the boat above the water line while underwater the water was pushing on the other side of the boat in the other direction - result: instant flip of boat.
A similar effect can be felt in non-breaking waves at sea - there is a movement of water within every wave, whether breaking or not, which you can definitely feel and I imagine (though I have never experienced this myself despite having been out in some pretty big seas) it might have enough force to cause a side-on kayak to flip even if the wave was not breaking - and possibly the tendency to flip might be exacerbated by having mirage drive fins extended under the water.
So personally I think that the problems described in this thread are not to do with any particular instability in Hobie's kayaks. Rather the issue is the knowledge that waves (in particular breaking waves) and currents have huge power, and even small waves and relatively gentle currents can exert irresistible forces on a tiny little kayak. The key to avoiding the risks inherent in these powerful forces playing on your boat is to be aware of where they are and how they work and to learn techniques which will enable you to avoid putting your boat into situations where they have a free hand.