Falsifying a death certificate is against the law in the US.
Define "falsifying". I know from an almost unimpeachable source that many doctors in the U.S. will simply write "myocardial infarction" as the cause of death, even if the real cause of death was something like pneumonia, because (a) it's a lot simpler to code in - just one code for a heart attack, whereas entering pneumonia will lead to a series of questions about what type of pneumonia, where was it caught, what was done about it, etc, and (b) it raises fewer liability questions for the doctor (annual review, or licensing review) and the hospital (liability for wrongful death) because a heart attack generally can't be caught from hospital-borne infection, but pneumonia certainly can.
I can't, and won't, disclose my source because it's a personal family friend, so I can't fault if one wants to discount my story; that being said, it happens all the time in the U.S. as well.
But if the doctor calling the fact and time of death writes it down as myocardial infarction, who's going to question that? Certainly by the time any questions might come up, most of the evidence will have been destroyed, one way or the other.