Nope. It is (from a frequentist's model of statistics), exactly what the article is claiming it isn't: If the model is true, and we repeat the experiment several times, 95% of the intervals we calculate will contain the true value. The actual CI you get in each experiment will differ.
Another discrepancy between frequentists statistics and the article is that yes, the values at the boundary of your interval are as credible as in the center.
Another discrepancy between frequentists statistics and the article is that yes, the values at the boundary of your interval are as credible as in the center.