I've never been approached to do it for an existing website
Its always been part of work I've done for them whether its web re-design or a new website.
But never say never.
A video review of the site seems like a really good idea, you know you get to see the problems, and hear the persons views and comments, sometimes i find its easier to visually see what someone it talking about than to just try and see it on paper.
however If a company approached me doing all that, I'd have a feeling I'd be getting a fairly large bill with is as well.
You can use Adobe Captivate to do this as well, it can record your screen, or the program you are using, then allow you to add tooltips, voiceovers etc, very useful for software demo's
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