You said, "which is required by law", then pointed to an FAA regulation, which is not the same thing.
Actually, 47CFR91.21 is a law. It is not just an FAA regulation, it is a law in a section of the code that is allocated to the FAA.
And on top of that, it references that it's a carrier decision, making that a fairly worthless thing to point to without fully examining carrier restrictions.
Until recently, the carriers opted on the side of safety and did not allow use of personal electronic devices (PED). I've actually had the waitresses, I mean stewardsesses, I mean flight attendants tell me to turn off my noise cancelling headphones because they saw the little red light on them. This ignores the fact that those headphones operate only at audio frequencies (no RF interference) and allow the passenger the ability to actually hear and understand the cabin announcements (like the safety briefing). So, I covered the red light with a bit of tape and they left me alone after that.
Now they allow small devices during all phases, and larger devices (like laptops) above 10,000', but still no cellphone service. Some are putting in local cells, but I've not come across that yet.
The problem is, the law he referenced does NOT say what he claims it does. It does not mandate that "airplane mode" disable the GPS. It says nothing about "airplane mode".
Your bolding for the United statement also missed the previous word, which is radio. Nowhere on the United page does it cover GPS,
GPS is radio. How do you think the signals get from the satellites to your cellphone?
that doesn't overlap with any of the more common definitions of radio being shortwave, AM, FM, etc.
I'm sorry, but "radio" does not mean just "shortwave, AM, FM". It means "radio". And in 91.21 terms, it doesn't say "radio", it says "electronic devices". The REASON behind "electronic devices" is based on RF interference from radios.
I'll also point out that although the frequencies that GPS are transmitted on doesn't mean the receiver cannot generate interference on many frequencies in many bands. I have a GPS installed under the backseat of my car that I cannot use because it emits interference right on top of a local amateur 2m repeater channel, making that channel useless.