I said nothing about position. But a lot of things measured have to do with how the structure of the aircraft responds to turbulence, rough air, and aeroacoustic vibration (aka flutter). So there might be modes where structural components have harmonics that are pretty high (several hundred to over 1000 Hz). Therefore you must use a transducer that has a frequency response that can cover that range, and sample the output of the transducer at least twice that rate (at an absolute theoretical minimum, but rule of thumb is 5x oversampling).

Possibly he might measure some other thing, but still after your question I started to wonder how much a passenger plane moves per thousandth of a second.

So: some quick googling suggests that "economical cruising speed" of an Airbus A320 is 840km/h [1]. After quick back-of-envelope calculations, this gives ~230m/s, so 0.2m per 0.001s. Given some possible uncertainty of a single measurement, I'd imagine that's not unreasonable level of precision when e.g. your Airbus is landing on an airport.

[1]: http://www.airliners.net/aircraft-data/stats.main?id=23