Well you could interpret this in a number of ways.
For a poorer Oxbridge grad , maybe whose parents didn't even go to university teaching is a step up. But then the argument for 'social mobility' in a 'better than other universities' way doesn't hold water. Maybe these people genuinely want to give back? Or they don't want to aim high? Or, the supposed benefits of Oxbridge in launching ambitions didn't hold true for them, for whatever reason? Who knows?
Only 8% going straight into employment. While many may be interested in 'other areas' because they didn't get training contracts (a lot of which is big transactions for commercial law) family, criminal law etc are the ones actually going to court and the people who will become barristers. Which is what 99% of the general public think lawyers do anyway. I doubt that they're claiming grads want to work pro bono for legal aid, I mean look at Amal Clooney's glittering career (an Oxford grad). She did do an LLM after university.
Finally, it does say public service, which doesn't tie in with the earlier information. You are correct, it is survey based which means the responses depend on those who bothered to reply.
The Fast Stream isn't the most prestigious or competitive of Civil Service roles, 'full rotation and training' aside. It really depends on which stream exactly. It even has things like HR and some of the schemes don't even require a 2:1 only a 2:2. Specialist entry level roles like policy advisor or positions in the diplomatic service are also available and more competitive because, unlike the graduate scheme with structure interview processes and multiple roles, these need one or two people for a specific job, and the interview process is less structured.