There's all these studies out there that suggest vegetarians have lower rates of just about all kinds of cancer.

Right, there are all kinds of studies.

Is your question whether anyone on AMHD can disprove "all kinds of studies"?

No I was just looking for information on AMHD in vegetarianism and health in general.

"We" read the same research you do.

Possibly, maybe even probably.
Just remember that it's extremely difficult to do dietary studies, because people bring countless other variables into the equation.
Vegetarians (by choice rather than poverty) tend to be health conscious in general, so how would you plan a study and eliminate all the 'bad habits' associated with one group vs the other?
It is known that certain things about animal meats are not good, such as taking longer to digest than we were designed for, and that meat and dairy products and eggs are high in 'bad' cholesterol. They do provide protein, a few vitamins, and iron that are more work to get in vegetables. Studies seem to show that onions and garlic are good when eaten with meats to break them down. And so on. It depends, it depends...

Studies of entire cultures with similar diets overall tend to be a bit more revealing. Some countries where cattle raising is the main industry have high intestinal cancer rates, and even very poor countries who have nothing but rice and beans to live on have low rates, and that tells us something, but then they die of other things.

There's some confusion about the definition of vegetarian, so people who also eat no dairy or eggs are called vegan.

(I limit beef and pork and lamb, but eat chicken and fish and dairy, and make sure to have fresh vegetables.)

Lower meat intake is more generally healty. Of course there are studies that show a all meat diet, or a all fish diet is best, A study is just as good as the money you pay the person doing the study

This is one of those things that you'll need to read up on if you're interested. There's so much information out there, and unless you're actually interested in it, it's a lot of work for no gain.

We volunteer here, so really, we're not going to read the studies for you, or do research for you, if that's what you're asking.

Time to do some work if this is something you're really interested in pursuing.

I've read a "Mediterranean diet" is good for general health and for forestalling heart attacks and strokes and high blood pressure.

Mayo Clinic -- Mediterranean diet