Well, whichever one checked first, the point still holds. Checking is not a free operation and you should expect it to have consequences and it to affect Uber's demand forecasts etc., and affect other price quotes. You do not have independence here and so the comparison is not as meaningful as it seems. As the Roman wit said, "when two people do the same thing, it's not the same thing."

(The right way to do this is to randomize multiple independent occasions - wait until one of you was about to call an Uber, immediately flip a coin to decide who does, each time checking you or your wife's Uber, and never both, and compare the long-run average.)

> with an apologetic confirmation dialog, possibly only after some holding period has timed out

Right. I've seen the same thing myself. They would prefer not to apologize to the customer because they changed the price, because it is in fact annoying and a bad customer experience. So the prices are surely carefully set in many ways with an eye towards not changing as much as possible.

> This enables people to construct a plausible story to explain any price.

Indeed. So you should mention one of the most plausible stories if you're going to list a bunch of them.