this topic keeps popping up every month or so and there have been some really useful and helpful insights into the topic so if you did a search it would throw up loads of good stuff.
in summary, Cat D's and Cat C's are all relative. An insurance company can classify any car as anything it wants, they are not supposed to as they have strict guidelines to follow!! it all depends on what suits them at the time. Also, the Cat classification is relative to the value of the car, for example if a car is worth 200, and it sustains 150quids worth of damage, an insurance company isnt going to repair it or put it as a Cat D! yet according to the technical language of a Cat D, it is possible, yet in real life it wont happen. similarly if you have a 150,000 pound supercar and have a big crash that will cost 50,000+ to repair it can be classed as a Cat D with light damage etc... as the repair costs are small when compared to the replacement costs of the vehicle.
Personally i have had quite a few insurance written off cars, ive repaired quite a few myself so i know there are pro's and con's to doing it, but how do you know the car you are buying hasnt had substantial damage that has been repaired but not recorded on the log book or hpi register? if you are prepared to wait a little longer to get the car fixed and then be prepared to sell it for less than a 'straight' version then you can't go wrong in my opinion, just choose your car carefully, i.e. try to avoid any car with chassis damage which requires jigging work, as its costly and time consuming.
I emailed a similar guy on ebay and he told me it was a Cat B so i told him that was illegal, he told me it wasnt, so i sent him the link to the DVLA website and the VOSA website where it stipulates as such and he disappeared?!? haha
and yes, only Cat C require a VIC (Vehicle Identity Check) this is basically to makesure the car being repaired is the car that was damaged, i.e. the id hasnt been used on a stolen car, so there has to be evidence of repair. it isnt a roadworthy check as the car has to have passed an MOT before it has a VIC (if older than 3 years).
my advice, take a mechanic with you, or get them to show before and after pics to document what happened and what has been done. happy hunting!