Overlapping confidence intervals does not mean > x% chance that the two variables' expected values are the same. If the intervals overlap, the difference is not statistically significant.
Your example about random variables is largely misinformed. You're talking about things as if they are individual values. But we're talking about sample means. The probability that a sample mean for a large sample is above the 90th percentile is massively lower than 10%, and depends on n. The joint probability of getting two sample means above X threshold is irrelevant.
Confidence intervals don't tell you what the probability of the true mean being above X is. They tell you, bluntly, the range of values where the true mean could be, with 95% confidence ("If i were to do this experiment 100 times, based on the results I got, I would expect the true mean to be within this range")
You can play with some numbers and methods but you can rest pretty sure that a material effect size is probably not rigorously evidenced if the intervals overlap