As I said, it wouldn’t matter in this particular case — I was simply pointing out that they probably have a rule like that for good reason, in case someone wanted to try to argue that the rule was in place simply so nobody would be able to see Adam’s body, as part of the conspiracy.
On the other hand, if I were part of the Lanza family, and wanted to join the conspiracy in order to get Adam off for the crime, I might use this as conspiracy evidence that the police were letting people tamper with Adam’s body to plant evidence that he was shooting.
Because certainly they could have examined his body and found that there was no evidence that he shot any weapons that day, if he wasn’t the shooter. You might want to prove he was murdered, instead of having committed suicide. Coroners do that all the time, you can often tell whether a shot was self-inflicted or not, but if the evidence was tampered with you would have trouble taking it to court.