I like your "describing the beach" analogy, but you perhaps give astrophysicists/cosmologists less credit than they deserve. We certainly do have to do a lot of extrapolation to say anything about distant stars, galaxies etc, but we do get some breaks. An obvious example is emission lines: you can take a sample of gas in the lab, pass a current through it, and look at the frequencies of light it gives off. That list of frequencies gives you a 'fingerprint' for the gas you're looking at, and it's well understood in terms of quantum mechanics.
Now, when we look at distant stars or galaxies, we see exactly those same series of lines (modified systematically by redshift as appropriate), which tells us that quantum mechanics works the same in those stars/galaxies as it does here on earth.
At the same time, there is still a huge potential for uncertainty when trying to get more specific information, which is what makes astronomy/astrophysics so hard (and interesting :-). The Hubble constant issue that brought this up is a nice example: The WMAP results constrain H very tightly, and therefore, if there's no dark energy or cosmological constant, the predicted age of the universe (it's just 1/H, although the weird astrophysics units of km/s/Mpc seem designed to make that non-obvious) can be found very precisely - that is, with a small 'statistical' uncertainty - it may not necessarily be very *accurate* - that is, the reported value is close to the true value.
That might seem done and dusted, but as others have pointed out, there are other ways of constraining the age of the universe. An obvious way of getting a lower bound is to look at the oldest things we can find. Globular clusters are believed to be very old, and by modelling the evolution of these galaxies suggests that they're older than the age given by 1/H.
It's further complicated by things like the results of the High z supernova search, which suggests the universe is accelerating in its expansion, and so 1/H isn't a good measure of the age of the universe.
So, given all that, which do we believe, and how do you summarize the "age of the universe" in one number? Answers on a postcard to any well-regarded, peer-reviewed astrophysical journal...
