You seem to not understand how botulism works. It is impossible for vultures (or anybody else) to get botulism from a carcass.
First, you have spores. They are ubiquitous in nature, and you have probably eaten lots of them. They are especially common on vegetables growing around/in dirt, like garlic. The spores are
- indestructible when using common cooking methods
- dormant under normal food storage conditions
- not dangerous to humans above 1 year of age. They remain dormant in the human body and get excreted without causing anything.
Then, you have botulinum bacteria colonies. To get a colony going, you need to take some spores and cut off the oxygen supply. For example, storing raw garlic in oil provides both a possible contamination route and a perfect growth environment.
The bacteria themselves are
- easy to kill off with heat
- not prone to establishing a colony in your body.
The problem with the bacteria: Once there has been a colony, it starts producing the toxin. This toxin is very poisonous even in minute amounts, and stays around to harm you even after you have killed the bacteria which produced it (e.g. with acid). It is not especially heat stable, certainly not as stable as the spores.
So, the way you get botulism is:
- Start out with food contaminated by the spores (meat is rarely such food, vegetables are more common. Of course, cross contamination in your kitchen is possible.)
- Cut off all oxygen supply for some time. A colony forms.
- Sterilizing the food by placing it in boiling water for some time doesn't matter, the spores will survive it easily. (This is why industrial food is canned at much higher temperatures, and safe home canning recipes are quite acidic).
- eat the food after it has been stored with the colony inside.
So, vultures don't have any special resistance to botulism toxin, they just don't come in contact with it.
On a side note, there are quite a few other pathogens which are common in meat, and vultures are probably more resistant to them than humans. But it is normal for bacteria to be able to only make one species, or a small range of species sick. Just ask the poor medical researchers trying to heal human disease in mouse models - there are huge differences.