As Jacko and others have pointed out previously, the 'arms deal' or is that 'strategic defence relationship' that was AY, was actually negotiated between the UK and Saudi governments. The subsequent contract was signed between the two governments.
Not at all sure how the alleged bribery by BAE would have impacted on that. And still can't quite work out how you can bribe a customer with that same customer's own money and apparently with its own money!
Later media reports today say Turner was allowed to continue his travels in the US and is now back in the UK. Guess it couldn't have been such a major issue really.