If each individual shot has a 0.1 chance of going in then you'd expect a goal on average every 10 shots.
That's not misleading, it's basic probability exactly the same way as saying that rolling a six on a fair dice happens about every six rolls. Now, probabilities don't work very neatly in practice so you'd see things like someone scoring three 0.1's in a row where another striker might have missed 20 in a row, but over a large enough sample size it'll be about right.
The problem is with your assumptions. Shots from 25yds go in far less frequently than 0.1. And secondly, can you imagine a team allowing someone to have twenty shots from the edge of the box in a game?
The maths is essentially proven. You can demonstrate it with coin flips, dice rolls, or any other repeatable chance event. The only problem that XG has is the samples used to determine the value given to any given chance because, unfortunately, that has to come down to a set of selection criteria that will either be subjective, missing, or very hard to factor in. Minor things like distance from goal and the angle to the goal are easy to do, but you could come up with all sorts of other criteria that will have an effect like weather conditions, pitch quality, pressure from defenders, lighting, and so on. All those things will have some impact on the "true" probability of a shot going in but may be impractical to take account of due to either measurement or sample size issues.
So it's not a question of "can we model shots on goal mathematically?". It's a question of how well we can model it. And XG seems to be a pretty good predictor of results.