The truth is that it depends on who you get, I had a car where it came with no V5C but was on the data base and I had the reg number and chassis number, however, the chassis number on the car ended in 5 and the DVLA had it ending in 6. To make matters worse the reg number was on the heritage certificate but they had a C wher the actual reg had a G.
I had a very negative responce until I spoke to one person and laid it all out, a 5 could be mistaken for a 6 when they computerised the records and how likely is it that two identical cars with chassis numbers one digit apart had reg numbers that were identical apart from one character which meant one would have been registered in London and the other in Leeds (if I remember correctly).
He agreed and the next thing I had a new logbook with the correct chassis number, it just depends on who you get and how reasonable they are (and perhaps how you approach/speak to them).