It may not matter what UA's policy is anyways if you're flying a UX carrier. Each of the UX carriers has its own policies for safety and general flight ops, so even if UA allows NC headphones during the whole flight, your particular UX operating carrier may not.

The big problem is that there's no standard for certifying devices as non-interfering, i.e. safe to use at any time on board an aircraft. While we all know (or think we know) that our devices are safe, there's no way for a flight attendant to know whether my headphones have a radio built into them (or something else that could potentially cause interference). From what I've seen, they're starting to have a similar problem with PDA cell phones; FA's can't tell whether the transmit function is actually off because each device is different.

Whlie interference is unlikely for the vast majority of devices people are likely to try to use on a plane, it seems to make sense to me to err on the side of caution, rather than hoping that no one happens to bring on board something that does happen interfere with the plane's equipment. The best way around this, IMO, would be for the FAA to set standards for non-interfering devices, with a process for verifying that the devices are compliant, and then allow manufacturers whose device met the requirements to put a big "FAA approved" stamp on the case, just like UL or FCC standards.

On the other hand, I guess that not being able to use electronic devices for 20 minutes is not a big enough deal to make it worthwhile. Plus, as other posters have noted, there are probably other safety reasons that you'd want most devices (video games, iPods, etc.) turned off during takeoff & landing, anyways.