It's not uncommon to get cell service on a mountain peak, even one that is very remote.Is this a misunderstanding/misprint? I cant see there would be any cell phone connectivity on Eagle Peak due to its remote location and rugged terrain likely to be very limited if nonexistent.
For the same reason that at a top of a mountain you can see views that stretch for miles, you can also get a clear, unobstructed path between the cell tower and phone.
Of course, it depends on many factors, like weather, cell tower strength, etc but I've experienced this many times. No service on the hike up a mountain, but suddenly at the summit my phone starts buzzing and I begin receiving a bunch of emails / texts.
Edit - I just looked it up, and in ideal conditions, with no barriers, a cell tower can reach phones that are 45 miles away. More typically, towers only get 1-3 miles of coverage (or less in urban areas). But that's generally because we're not in direct line-of-sight and the signals have to pass through multiple obstructions as well as interference from other signals.

Cell Tower Range: How Far Do They Reach?
Wireless networks transmit voice and data signals over cell towers, using a range of radio frequencies, that can reach a customer’s cell phone far away.

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