CAT D Vehicle rules/paperwork?

[ginge191]

If its a previous cat d you don't need paperwork, but it will be stated on the V5.

If its current cat d they won't issue log book without a vic check (personal experience last year).

the vehicle, since the CAT D, has passed an MOT also; would this not be affected by a illegitimate V5? Or, would that be, as you say, a 'previous' CAT D? 
little confused; how is a vehicle currently or previously a CAT D?