can one state that true population proportion is between 90 – 93%?
In fact neither component works that way alone
A confidence interval doesn't let you state that the true population proportion lies inside the interval. Confidence intervals allow you to make a probability statement, but it's not even about the probability that the true proportion lies in the interval.
A failure to reject the null doesn't tell you that the null is actually true, it just tells you that the probability of observing a sample proportion at least that small given the true $p$ was at least $0.9$ isn't very small.
So there's really no reason to think that the two together would suddenly confer the ability to make the kind of claim the two kinds of analysis wouldn't give you on their own.