I must admit that I enjoyed the direction this thread took. Not many threads like it on TCLA!
Going back to the core issue, I think that it's well worth hitting up the law firm if you're getting rejected so soon and without a clear reason as to why this may possibly be the case (e.g. them filling up ACs, not meeting minimum criteria, typos or blank answers, 2.2s, etc). I've personally seen grad rec and the systems they use mess up too many times for me to put any faith in these sort of decisions.
I had been rejected from HSF on the basis of not doing their online assessment when it turned out that I had done it and they simply hadn't received the results.
Linklaters cut me off and then decided to pass me for their WG. A bunch of firms have failed to send me links to tests or VIs in time for me to complete them. I've also had problems with my foreign qualifications despite the British Council issuing an equivalence notice about them. One SC firm auto-rejected me because they thought that my UCAS tarif of 200-something under the new system failed to meet their minimum requirement of 340 under the old one.
Lest you think I'm venting, the point is that the process is set up and maintained by humans, and that mistakes can occur. If I faced the circumstances faced by the users who got rejected by NRF and had nothing to lose (e.g. because I wasn't planning on reapplying there), I'd be hitting up grad rec asap. Obviously, there's no point in asking for an explanation for a 'regular' rejection that comes after a few weeks when your application has actually been read.