I think it's more accurate to say that he coordinates the setting of policies and priorities and budgets. It's pretty useful for the NASA administrator to have multiple degrees because it gave him "street credibility" with the various centers of power within the the science establishment. Astrophysicists and aerospace companies are generally trying to cut each others throats with the NASA budget, so having someone with a leg in both worlds is useful.
It happens quite a bit that people with technical degrees with either formally or informally get training in business administration. Once you reach a certain level in academia, it's pretty much impossible not to be at least a part-time bureaucrat and salesman.
So I think you'll find it a lot easier as a lawyer, if you somehow figure out a way of using your legal skills in physics. If you have a law degree and a masters of physics or engineering, I can think of several unique job opportunities (legal counsel for a national lab or forensic engineering).