It really depends on how much overdraft he was asking for? If it was only £100 or so, I couldn't see there would be a problem. If he was after several thousand then they, probably quite rightly, turned it down.
Quoting a turnover is pretty much irrelevant, especially an estimated one. Is the business profitable so far? - it's relatively easy to turn over a lot of money, but making a profit is the important thing. He will also, presumably, have no accounts to show as he's only been trading 6 months. Maybe the bank don't agree that his business plan will show a turnover of £250,000 and that he'll make some profit out of it.
If the business is going so well after only 6 months, I expect the bank would be asking why he needs an overdraft when he didn't previously.
As to why they've searched his credit history, such as it is, so often is a question only they can answer.
Does he have a business advisor at Nat West? They usually give you one when you start a company and bank with them. Ours was actually quite helpful and would have answered this sort of thing on the phone without needing a meeting. In fact an application for an overdraft or credit/debit card, loan etc would have gone through them and not through the branch. We've moved away from Nat West now to one of the 'free' banks but have to say they did give decent advice when we were starting off.