Well, see, here's the deal:
Let's say you have two closely related species. Oh, I dunno, say a horse and a zebra. Now, presumably, there is some subset of useless genetic material (according to our current understanding) that was bequethed to both by their closest immediate ancestor but which has no reason to be conserved.
OK, one would then expect that those regions would diverge at whatever rate random mutations take place. However, it seems unreasonable that this would happen instantly. Therefore, there would be some reason to expect that some percentage of those regions would remain common between the two, though diminishing over time.
So, I guess that's my question: could some percentage of conserved regions be due to random circumstance - i.e., they just haven't had enough time to mutate apart.
Now, obviously the problem is that we're talking about vast spans of time and multiple intervening species and two long-divergent branches of the phylogenetic tree when comparing, say, man and mouse. So, like I said, I more or less agree with you that random chance would not conserve much of anything.
So, leaving apart some unidentified yet crucial function (the route being explored by this research above) my next question would be: what processes might impact either the longitudinal or the temporal uniformity of genomic mutation. The answer likely rests in that (if those conserved regions in fact have no function).
The article has a quote which addresses your question.
Haussler's team recently described "ultra-conserved regions" in mammals. The level of conservation was even higher than that for many genes. "What's most mysterious is that we don't know any molecular mechanism that would demand conservation like this," Haussler says.