As long as you remember you still have those rights, it doesn't really matter?
Also, people have a natural tendency toward defending themselves after being accused. Being read your rights is a reminder, in the heat of the moment, that no, you don't have to talk and you have the right not to. And your right to remain silent is important even if you're not guilty (maybe especially!). Dont Talk to Police: http://www.youtube.com/watch?v=6wXkI4t7nuc
References:
[1] Think Progress - http://goo.gl/DPV6L [2] Wall Street Journal - http://goo.gl/fEPnO
Now where did you buy those pressure cookers, hmm?
But in this case, certainly they should ensure he doesn't die due to lack of medical attention while they attempt to read him his Miranda rights.