When you cut the outside of a barrel on a heavy duty lathe with extra barrel support locations, it is pretty easy to imagine that this machining is very tight.
Even the best tooling starts to flex once you get more than 5 or 6 diameters inside of a hole. I am not a machinist, but watching some of them work, it looks like even a high end, large diameter reamer is still largely following the original drilled hole, just cleaning it up. It seems like this would be largely true regardless of using a button or machined rifling (but that is a guess on my part)
I am always amazed that the barrel making process works so well. Obviously, multiple companies have been very successful making barrels using several methods.
I suspect that the button rifling process is somewhat similar to roll form tapping. The cold formed steel actually improves in yield strength and wear resistance from the deformation process, while a cutting thread process does not.
Wikipedia.org has a good article on it.