Demonstrably false. Obvious counterexample: the study in the OP, which has overlapping confidence intervals and a statistically significant difference.
Proof: just calculate the 95% confidence interval for the difference between the two means. You can figure out what the stddev was from half the confidence interval divided by the z-score for a 95% confidence interval, 1.96, and you get 1.02 and 1.30 for the two groups. Then the confidence interval is: (10.4 - 6.3) +/- 1.96*sqrt(1.02^2 + 1.30^2) gives [0.86, 7.34]. This does not include 0, therefore the difference is significant.
> The probability that a sample mean for a large sample is above the 90th percentile is massively lower than 10%, and depends on n.
I was trying to give a basic intuition about normal distributions with a simple example, the distribution of one sample is a simpler example of a different normal distribution. Yes obviously the distribution of an estimate of X given lots of samples is not the same as the distribution of a single sample, I never claimed it was.