True, I should have qualified that statement to exclude spy satellites, which obviously offer much higher resolution than the commercial satellites in operation. which to the best of my knowledge are incapable of resolving objects less that a few metres across.
Resolution is a much misunderstood concept anyway (ask ten Leica fans to define it and you'll get at least five different answers!). A much better method (and indeed the primary scientific method) for describing the quality of an optical system is the Modulation Transfer Function (MTF), which is simply a description of the spatial frequency response of the lens system. So we can say that a lens delivers a certain contrast ratio (in percent) at a given frequency (usually line pairs per mm at the image plane).
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They have an imaging resolution of 5-6 inches, which means they can see something 5 inches or larger on the ground.
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This is a confusing statement. When one talks about resolution one normally refers to the maximum spatial frequency that is transferred with a contrast ratio of at least a defined value (often 20% but this figure is almost arbitrarily chosen). In other words, resolution is generally taken to be how small the line pairs can get before they blur into one grey mess, like so:
But the contrast ratio of any lens drops as spatial frequency increases, so by simply choosing an object with higher contrast in the first place, the resolution is increased (this is why resolution is so useless for describing lens performance). For this reason resolution is often tested at a particularly high object contrast ratio, usually 1000:1. But a person walking down the street, viewed from a satellite's position in space, is far less than 1000 times brighter or darker than the street.
So it's not accurate to say that a satellite that can just about detect an object 5 inches across against a uniform background (representing the object as a blur of just discernable contrast) actually has a resolution of 5 inches. When people think "wow, 5 inches!" they might imagine clear photos of their small dog sleeping in the garden. In reality such a dog would not be remotely identifiable as a dog. In fact, it's very possible that the dog would not even appear as a smudge on the photo, because for all we know they might mean a 5-inch object with a contrast ratio in excess of 1000000:1 (e.g. a spotlight shining upwards) rather than a dog on grass with a contrast ratio of perhaps 10:1.