I think there are two things you might be missing, although one is subjective.
First, by many accounts it is more time consuming going modular and often a lot more expensive than the £35,000 usually quoted. With Integrated coming in at £61,000 and all nicely packaged to stay current and continuous, there may be an advantage there - it takes a lot of the hard administrative work out of getting a fATPL (rightly or wrongly).
Second (and subjective); it is often said that knowing people in the industry will give you a big step ahead in getting "that job". By proxy, the big integrated schools seem to somewhat akin to that the old family friend or great Uncle who knows the head of recruitment at BA. The airline come to them and they put names forward. When the competition is all about getting your CV to the top of the pile, I can't help feel integrated offers that, whereas modular falls short.
Regardless, of whether you are paying £35,000 or £60,000, if you can't get a job at the end of it you are utterly screwed. If I felt the extra £20-30K was going to secure me the job (a backhander you might call it), then that would swing it for me.
As a disclaimer, I am in no way naturally biased one way or the other, and broadly agree that the best way to the left-seat of a 747 should be via a decade or two spent in bug smashers and turbo-props. The reality just doesn't seem to match that though, and while the evidence to support Oxford's claims of success are a little sketchy, I fail to see any evidence to the contrary, nor any competitors even being in a position to make similar claims.
The difference between flying and the lawyer/doctor scenario, is it seems more likely that a law firm or surgery awaits you at the end of the degree. In aviation on the other hand, you complete a course costing as much as twice the normal fee for a degree and come out with nothing more than a pilots licence. A BA/BSc will at least open doors in all kinds of sectors. A fATPL does not grant that.