The question here is what do we mean when we say "a reasonably fit man could run a x:xx mile with training"? I think it has wildly different answers depending on your assumptions.
Case A: "Don't be afraid. You have found favor with God. You will become pregnant, give birth to a son. He will be a great man, and upon his shoulders will lie the fate of humanity. For if he can run a 5:00 mile under legal conditions by the age of 40, all of Jacob's people will be saved. And if not, the people of Jacob will be cast down into the furnace of fire to be tormented forever and ever. I have given word of this miracle to the political and religious leaders of this land, and have made a post on letsrun.com."
I think under these circumstances the vast majority of guys would be able to do it. The best coaching, diet, and lifestyle possible from conception on. Every legal supplement, a fluffle of rabbits, and talk about motivation! I think we see success in almost every case.
Case B: "Dude, you know what I'm going to do to mix up my life as a sedentary, unathletic 37-year old insurance salesman with a horrible diet and bad ankles? I'm going to train to run a 6:00 mile. I'm skinny enough, and I do play basketball once a week. My mom's friend has this training plan she says is great, so I think I'm going to try that for a few months. And hey, want to get a few pints after work tonight? I'll be off around 7:00."
Probably not happening...
Could the 37-year-old guy get down to 6:00? Maybe...if he decided to devote his life to it for several years. He might want to quit his job, get surgery on his ankles, pay for professional coaching, and gradually build up to 50 miles per week with speedwork. Then it couldn't hurt to get a couple of fast friends to pace him at 90-second pace, and cheer him on as he kicks for home. But he's so far behind, I think he'd have to be reasonably talented to get under 6:00 even then...