I just listened to those John Denver clips and I think you're out by a tone - comparing it to a tuner, those notes you're calling A4s and B4s are actually G4s and A4s. Not that that matters, he's still got an impressive range.

I can hit those notes in chest voice on a good day, when I've been practicing and when I have properly warmed up. I also find that there's a region around where my chest voice turns into my head voice wherein I can do reasonably convincing, well-supported composites of the two voices that sound more chesty than falsetto-ey.