It's also why we can detect muons on Earth, a particle that would have decayed by the time it reaches us if its age depended on our frame of reference.
I looked up after your reply, they decay by losing energy based on the matter they interact with. So in the vacuum of space they can travel great distances as long as they don't interact with the matter.
You are misreading the document. The muons are created in the top of the atmosphere and decays after a very short amount of time. The point is that they decay so fast that they shouldn't be able to reach the ground. They manage to do that because time passes much slower for the muon. Or to put it differently, from the point of view of the muon the thickness of the atmosphere has been compressed to become much smaller than from the point of view of an observer on Earth.
You are right, I misread the document. I stand corrected.