Just because the halting problem can not be solved in the general case, does not mean it can't be solved for a specific program.
So the conclusion with the heart are wrong. The "program" that is a heart might be analyzable as a halting problem. It's not a general purpose program after all - it's a specific one.
Not to mention that the human heart has a finite number of cells. The amount of "memory" (or whatever word you use for the heat) is finite, making it a DFA/FSM not a Turing machine.
You could argue that the number of cells is so huge that we might as well treat it like a Turing Machine, but given that the researchers were simulating the human heart, I'd disagree with that.
Knowing that the human heart weights on average 300g, it makes about 10^(10(+/-0.5)) cells, hence 2^(10^10) states for a FSM built on it (rough approximation).
Even though the simulated experiment had obviosuly less cells, I think that the real heart can in practice be considered as turing equivalent.
This must be one of the loudest screams for a good-looking, ultra-geekily designed T-shirt, ever. I'm thinking maybe something like this: <http://www.lafraise.com/Article/index/id/25>; but of course with NOR gates on the inside.
So the conclusion with the heart are wrong. The "program" that is a heart might be analyzable as a halting problem. It's not a general purpose program after all - it's a specific one.