Though I know there are bot flies that have no problem just eating flesh, the normal house fly seems to also cause a problem once further inside. But I never thought about the dead vs live flesh so I just did a little google search and some of what I found is this: 

attractive conditions:Moisture, warmth, and odor attract flies. If open sores are present, or if thick fur is dampened with urine or feces, flies will head toward these warm incubation areas to lay their eggs. The chances are greater if the rabbit is outside, but it only takes one fly indoors to do the damage.What kind of damage? Maggots do not stop at the surface. Once they have consumed external debris, they go right on to sound flesh (sometimes up the back where you don’t see it), and once in the flesh, they produce toxins that create a state of shock.

SOURCE: http://www.rabbit.org/journal/2-12/fly-strike.html

So maybe it’s that they end up just burrowing into the surface and create a toxin.  I will continue to research the details but as gross as this is…and it is GROSS to research….you’ve got me now questioning and I want to know.  Yuck! THANKS! 

UPDATE: Okay….so far, at least from what I’ve been reading about flies –  though there are types of flies/larvea that are flesh eating, most commonly they just “infest” live tissue to develop through the larvae stages.   But that can cause shock in a rabbit very quickly.  

Now of course, I’m not expert, this is not from some real in depth research – just from a little googlearch so I could be way off base, but that is what I gathered….so far.   

Gack….this could be my new diet plan – I don’t feel like eating after all of the photos and reading I’ve done so far. 

Well this site talks about blowflies being the common culprit in rabbits.
http://www.galensgarden.co.uk/herbi…strike.php

Quote-
Fly strike, or blowfly strike, is a serious condition, mainly affecting rabbits, that occurs during summer months. Fly strike is caused by flies; attracted to damp fur, urine, faeces or the odour of rabbit scent gland, lay their eggs on or around the rabbit’s rear end where they hatch within hours into a seething bunch of maggots that eat into the rabbit’s flesh, eating it alive and releasing toxins in the process.

This site talks about medical use.
http://news.nationalgeographic.com/news/2003/10/1024_031024_maggotmedicine.html

Page 1 quote –
Only a few species of fly larvae, primarily blowflies, are suitable for such duty.

Page 2 quote - 
John Church, an orthopedic surgeon and modern maggot medicine pioneer in the United Kingdom, says picking the right maggot for the job is key.
“Some maggots burrow deep into living flesh, but the ones we use do one thing—recycle organic waste,” he said.

They seem to both say blowflies & give them different eating habits so maybe it’s different types of blowfies???
The rabbit one does mention “Greenbottles” as the common type bothering rabbits.
The medical ones that only eat dead flesh must be a different type of blowfly.

This is form an article Dr. Patenberg did for North Texas Rabbit Sanctuary (The Indoor Rabbit):

We also see fly larvae (Cuterebra) and tapeworm infestation. This begins as eggs or larvae in the soil which then migrates through the skin to cause local abscesses and infection. In severe cases, brain or neurological damage may occur. Treatment often requires surgery or prolonged antibiotic therapy. Fly bites may carry pox virus, which can cause lesions that occlude the rabbits sight or breathing and make them vulnerable to infection. Shope’s fibroma is a tumor caused by a virus, carried by vectors (like flies), that is seen in rabbits.

By far the most common, and worst, thing we see is the bunny that comes in with maggots in its skin. This is usually around the rectal area, secondary to urine or feces getting on the fur, and flies laying eggs on the area. The result is usually a very sick rabbit with severe skin wounds and infection. Treatment usually involves anesthetizing the rabbit, removing the maggots, cleaning and debriding the wounds, treating with antibiotics, and LOTS of follow-up care by both the owner and the veterinarian.

_________________________________________

One of my friends rabbits got the cuterebra and it was a nasty thing – she innocently let her rabbit Maggie outside and luckily Dr. Patenberg discovered this nasty little creature and with daily follow up to the vet (who cleaned the wound) Maggie survived and my friend has never ever let her rabbits outside again.

Oh, good, I’m not alone in this icky search! Thank goodness.

Plus, from what I know about the medical use of maggots, They are used under controlled conditions – as in – Put on and then taken OFF once they have finished the job.

I assume that infestations in rabbits or other animals happen under uncontrolled conditions in which there are a multitude of co-existing primary issues ( like matted feces, poor health etc)

Makes me think about my childhood in North Carolina – we always wore shoes because of the issue of hookworm….Shudder.

*shivers*

I think the case is generally that they have been in an unsanitary conditions-like have pee on their bums or poopy bum and then they are at risk because of that? Obviously outdoor buns are at risk for it…but I don’t know if they need to be dirty bummed or not…Awful thing