it is possible, as i stated just below in my comment i'm simply not aware of any exceptions.
to be sure, i specifically selected cryptography in the very first comment for a specific reason. math subspecialties require rather unhealthy amounts of training that is best started as early as practically possible. it is very hard to do, a mentor often helps and speeds up the process, and by the time you start doing original research as a fully self-taught mathematician, well, you might as well get get some recognition of your efforts by way of getting a degree, plus potentially get funded to do it. why not?
due to several factors, in all probability, successful applicants for mathematical research (cryptology) positions will have a phd, if nothing else simply because prior original research is likely to be required. competition pushes up the entry barrier as high as possible, for better or worse, and so the exceptions in research without a phd are going to be exactly that - exceptions.
the school ranking is a bit of a red herring here. while reputation of the school itself does matter quite a bit of course despite everyone doing their best to pretend it doesn't (but insist on sending their kids to the best school possible), it is simply that very often talent is sought out from specific groups/departments/professors who just happen to teach at this institution, wherever they are located. it's just that most of the time large well known institutions have budgets and brand recognition that attracts top talent, often from around the world. brain drain is real.
just to be sure, its not that i recommend everyone goes out and gets a phd in math (personally, i think that even a masters degree is a complete waste of time for the vast majority of jobs), but that in some situations it is a de facto pre-requisite. it likely will not pay off financially and it is a big commitment that can crush you mentally, emotionally and potentially even physically. some departments have sadly a reputation for high suicide rates.
btw. john list does have a phd, and spent 8 years teaching elsewhere prior to UC. not sure if that supports your meritocracy argument, as one would think someone with his reputation today could advance quicker.