To the OP; I don't think it could happen. Heart attacks aren't total freak of nature events. Trying to induce one in someone who lived decades in good health IOTL after the POD isn't too plausible.
The more realistic way to do it would be to have Bush get killed in the actual attacks. The President isn't often in the Capitol and the White House is an extremely hard target, so either the Pentagon or the towers would be the ticket. Imagine that Bush due to some butterfly goes to New York (perhaps he is promoting some action related to the financial industry) and before he goes to the NYSC to make the speech eats breakfast with donors and bigshots in the Windows on the World restaurant at the top of the North Tower. The plane hits, the tower collapses, and he dies.
Now THAT is a timeline I would read.
Marine one would not hesitate to land on the top of the wtc, fire or no fire. Imagine those pictures with Bush covered in smoke running in the helicopter as it takes off from a burning building and then a president landing in an open area coming out from the helicopter covered in ash.