Manual data entry is just too unreliable and time-consuming. I don't see how this could work short of integrating OBD-II fuel consumption data combined with some sort of presence tracking.
I agree with you that at a large scale this is a problem. The one thing I decided very early on (when thinking about if/how I would grow this app beyond my family), is that this is for people who trust each other. If you don't trust the other people in your group to be responsible with the vehicle, then this app isn't gonna help. I'm trying to make the experience more smooth, not necessarily completely painless.
Regarding automatic tracking tho, the easiest option is Bluetooth based, the app knows the identity of the car, when the phone connects, it knows you're probably starting a trip. And the same goes for connected car APIs, those can much easier take the place of an OBD-II reader.
It's more hardware intense, but yes, add an rfid tag to each key, use a btle obd dongle, centralize computing in an arduino; phone home to a webserver the last logs.
Then at the end of the month debit each account that used negative gas.
The only thing this misses is encouraging fill-up before empty, but it could give notice when the tank is below ΒΌ before a trip
Regarding automatic tracking tho, the easiest option is Bluetooth based, the app knows the identity of the car, when the phone connects, it knows you're probably starting a trip. And the same goes for connected car APIs, those can much easier take the place of an OBD-II reader.