There are a multitude of factors that go into crime rates and what inspires people to commit them, but it is naive to believe ready access to guns is not a factor.
It is also naive to believe that it IS. A popular, oft-repeated, "truthy" sort of belief, but true only in that
every facet of life and society is "a factor" in crime rates.
There are big drivers of crime rates and there are small ones. Big drivers include things like poverty, education, enfranchisement, population density and average age, gender ratios in a given community, etc. Those actually have legitimate consequences for crime rates.
...
You may have a legitimate disagreement with Mr. Vaughn's short-hand way of phrasing this. To be more accurate he should have said
"Making illegal guns, drugs, the booze, ... won't rid the world of criminality." That's pretty inarguable.
There really is no case to discuss about "taking away" those things, as that's a physical impossibility as proven repeatedly throughout history. We might as well say "taking away race, culture, and religion won't end criminality." Doesn't compute. Can't happen. (At least not in the foreseeable near future.)
But almost all of us are guilty of conflating the phrases "making illegal for law-abiding citizens to have" and "taking away" in our less careful moments. They are not the same thing, so your quibble about what he literally said doesn't detract from the truth of the concept he was attempting to communicate.