Earlier quoted context omitted.
It's not "known nonsense", but not for the reason you think. There's a small risk of your phone connecting to some random carrier located in whatever country you're currently flying over. For some smaller / third-world countries, this can be quite expensive, cents-per-megabyte isn't unheard of.
Every time this is brought up people come out of the woodworks with post-hoc rationale for this rule that has no basis in historical fact. This comment is good example. Why would the FAA and other aviation regulatory agencies care about your phone bill?
The motivation is supposedly cellphones at high altitudes interfering with far-away cell towers that are reusing the same frequency at a distance that would normally make interference very unlikely, given the radio horizon and everything.
I highly doubt that that would still be an issue modern networks couldn't handle (also given that most other countries don't have a corresponding law on their books, as far as I know), yet here we are.
[1] https://www.law.cornell.edu/cfr/text/47/22.925
[2] https://www.faa.gov/documentLibrary/media/Advisory_Circular/...