I saw this story on NPR. Outside of the brief blurb, there's not much text.
So some googling turned up this link with a bit more detail.
Dr. Claude de Ville de Goyet, MD writes:
The myth that dead bodies cause a major risk of disease, as reiterated in all large natural disasters from the earthquake in Managua, Nicaragua (1972) to Hurricane Mitch, and now to the Turkish earthquake, is just that, a myth. The bodies of victims from earthquakes or other natural disasters do not present a public health risk of cholera, typhoid fever, or other plagues mentioned by misinformed medical doctors. In fact, the few occasional carriers of those communicable diseases who were unfortunate victims of the disaster are a far lesser threat to the public than they were while alive. Often overlooked is the unintended social consequence of the precipitous and unceremonious disposal of corpses. It constitutes just one more severe blow to the affected population, depriving them of their human right to honor the dead with a proper identification and burial. The legal and financial consequences of the lack of a death certificate will add to the suffering of the survivors for years to come. Moreover, focusing on the summary disposal, superficial "disinfection" with lime, mass burial, or cremation of corpses requires important human and material resources that instead should be allocated to those who survived and remain in critical condition.
Our experience in the aftermath of the earthquake in Mexico City showed that health authorities and the media can work together to inform the public, make possible the identification of the deceased, and the return of the bodies to the families in a climate free of unfounded fears of epidemics.
So the doctor seems to be saying that the risk to public health is minimal compared to the emotional and mental strain of seeing their loved ones end up in a mass grave.
Perhaps so; however I think they'd like seeing their loved ones picked apart by critters even less and watching them turn into bloated, gassy bags of slowly liquefying meat would be right out. In those cases where facilities aren't up to the job of storing a large number of corpses, mass burial might be the only option.
Either way, I don't expect I'll be keeping any corpses around. Can't be too careful, you know. ;-)