Best guesses:

> I had not even taken my phone out of flight mode yet, but somehow the app knew where I was, despite not having mobile service, wifi or bluetooth enabled.

None of which are GPS, which is likely what Uber used to know you had "touched down". And GPS, being "receive only" may not be disabled by "airplane mode".

> I also have settings for the application set to only allow location while the app is in use.

Is that a phone setting, or an app. internal setting (i.e., a setting inside the Uber app. itself)?

If it is a phone setting (external to the app) then this would imply that it may not really do what it says it does.

If the setting is inside the Uber app. itself, then that is just a "promise" by the app. developer that they will behave, and if it is this case, then they clearly did not behave.

Edit to add: Checking my android phone just now, GPS is not disabled by airplane mode.