Is it true to say a 90% confidence interval
"contains 90% of the means on average (as n of means goes to infinity)"?
I'm not quite sure what you're trying to say.
The correct interpretation of a confidence interval is based on repeated sampling. If samples of the same size are drawn repeatedly from a population and a 90% confidence interval is calculated from each sample, then 90% of these intervals should contain the population mean as the number of samples becomes large.