Contributed by Sara Sasse from Hatrack:
This risk has been known to be negligible for some time. The bacteria and viruses which cause infectious disease epidemics are propagated in living tissue — e.g., corpses don’t develop tuberculosis or cholera or malaria, for example.
Note that there are bacteria which act to decompose bodies, of course, and there is subsequent likely contamination of water supplies. However, that is not the same as propagating an infectious disease. The issue of potable water supply is a big enough concern in itself, but the risk of epidemics because of decomposing tissue isn’t.
Crowded facilities and poor hygiene facilities will increase the likelihood of epidemic spread of disease. Not because of dead bodies, but because of the living conditions of the live ones.
The WHO Pan-American Health Organization has a good summary as well as a general "myths and realities in disaster situations" article. The British Medical Journal also has a good summary article.