Iron is simply an element, so it cannot be destroyed by cooking (or generally temperature changes), as vitamins and other organic structures potentially can.
Cooked spinach inevitably has a much lower water content, thus the relative density of all other components must increase. So gram for gram, it makes sense that cooked spinach should have a higher concentration of iron (and possibly some other things) than raw. However, the actual process of cooking does nothing to change the amount of iron.
Judging by the nutrition information I can easily find (for example, from nutritiondata.self.com), frozen spinach is generally cooked by boiling and draining. That's pretty much what I'd have guessed; it's certainly the easy way to cook things.
Unfortunately, that means that some nutrients are lost with the discarded water. I doubt it'd be different for any other green leafy vegetable - though it's certainly much harder to find frozen mustard greens!
The nutrition information for fresh spinach is for fresh, raw spinach; if you boiled and drained it, you'd make the same sacrifice that the frozen spinach has.
As for your generalization, freezing vegetables and fruits does preserve most things pretty well - but only what's actually left in them when they get frozen! And while transporting fresh vegetables around can cost you some "freshness", it's not going to affect minerals. Some vitamins could be lost by breaking down (I'm not an expert here, but it seems possible) since they're more complex molecules, but minerals are just single elements. Those iron atoms won't fall out of the spinach on the way, and they're certainly not going to be transmuted, either!
Edit: Essentially what's been said in the comments is that the USDA nutrition facts say that "Spinach, frozen, chopped or leaf, cooked, boiled, drained" has about half as much iron as "Spinach, cooked, boiled, drained". A discrepancy, indeed, though not the same one cited in the question. My interpretation here is that the frozen spinach is simply not cooked in the same way (boiled and drained more thoroughly) as the non-frozen.
An alternative, proposed by Adisak, is that the frozen spinach nutrition means that you've taken the already-cooked, frozen spinach and boiled it again and drained away even more nutrients. This seems unlikely; frozen spinach is already cooked, so there's no reason for the nutrition information to assume that you'll boil it over again. The description (it seems to me) is referring to the cooking that took place before it was frozen.
Best Answer
You know, I have always liked to eat spinach with vinegar. Just steamed and with a splash of plain white vinegar. It is a very common way to eat spinach around here.
Anyway, I suppose it could have some affect on iron absorption. Large amounts of vitamin C can increase non-heme iron absorption by as much as 200%. This article, http://pubs.acs.org/doi/abs/10.1021/jf0203040, seems to indicate that acetic acid, the main component in vinegar, may also increase iron absorption.