Yes, he wants an apprentice rather than the finished article, but at the same time.... it makes a mockery of the whole process to not choose the person who seemed the strongest through the 12 weeks (yes, some will argue that they thought Lee was and fair enough... I just don't agree). Not to mention that clearly Claire wasn't the finished article when she came in as she's admitted herself that she's learned a lot and really changed her approach through the last 3 months.
Two abilities that would be HIGHLY desirable in any apprentice are the ability to handle pressure and the ability to present. Lee is going to be making a crapload of presentations and the fact is that even if he improves another 100%, he's never going to be very good at it. He was also clearly poor when it came to real pressure situations.
I liked him a lot and I think he seems like a great guy. But the flaws he does have would, I think, pose far greater problems given the likely style of job he's going to be doing for SAS, than the flaws Claire has.