Where are you getting the above from ie declining the invitation and unable to hit a barn door?
Sometimes people downplay their abilities eg a golfer who plays off scratch or has a low single digit handicap might say 'oh I'm alright on a good day' when in reality they are top few % in the world.
No, he DECLINED the offer according to Trevor Jones (the landlord of Chequers).
"at the beginning of July, Jeremy drove out to Oak Farm one evening and told Ann that he wanted to buy a five shot automatic 12 bore. When she asked him why, he replied: ‘I rather fancied myself as the country squire and thought I might go shooting.’1 Peter explained that it wasn’t the done thing and suggested he try one of his father’s guns before buying one himself. Jeremy later told detectives that his interest was due to the landlord of the Chequers inviting him to go pigeon shooting. Trevor Jones confirmed it, adding that Jeremy had declined his offer, saying he couldn’t hit a barn door."
Lee, Carol Ann. The Murders at White House Farm: Jeremy Bamber and the killing of his family. The definitive investigation. (p. 134). Pan Macmillan. Kindle Edition.