Everything you said is correct. This has always been a known problem for simple and ordinary kriging; you have to estimate the semivariogram from the data, but then you have to assume that your estimation is completely correct. In practice, this means that standard errors will almost always be underestimated.
This is one of several problems that we addressed with Empirical Bayesian Kriging in ArcGIS 10.1. Instead of estimating a single semivariogram and assuming it is correct, EBK simulates many semivariograms, so you end up with an entire spectrum that we weight by likelihood. By accounting for some uncertainty in the estimation of the semivariogram, this weighted spectrum does a much better job of estimating the covariance structure than relying on a single semivariogram. If you work with some data using ordinary, simple, and empirical Bayesian kriging, you'll notice that EBK usually gives larger standard errors than the others. This might seem like a disadvantage, but the larger standard errors will usually be more accurate. For example, if you use simple or ordinary kriging and make 90% confidence intervals, it will probably only capture 75% of the data, whereas 90% confidence intervals from EBK should capture closer to 90% of the data.