Probability is fundamentally all we have in science. The only distinction is in the level of confidence use in inference of the data. 95% is fairly typical though particle physics requires and impressive level >99.9999%
How would you denominate such a bet? I don't think money would have much value in a world where the sun failed to come up one day.
In science, what you’re talking about is not a “probability of being right”, but a probability of not getting the same experimental results completely randomly, without any underlying cause. You still might have 0% probability of being right. With “95% confidence” there still could be no measured effect whatsoever, you just made the same experiment multiple times and randomly finally got big enough random numbers to get you 95% confidence.
It’s not a nitpick, it is a serious mistake that 95% social scientists make.