With Uber, marking themselves as "arrived" does nothing but notify the passenger. I asked one driver about it and he says he does that a few blocks away because he doesn't want the text to be delayed.
The actual paid portion of the ride doesn't start until you enter the vehicle and the driver taps the Start Trip button.
You can also verify the entire trip later on your receipt. It shows the entire trip on a map, plus the start and end times, so you can verify that it matches your expectations.
