To test Krantz's assertion for recent Ph.D.s from U.S. universities, one can use statistical sampling. The American Mathematical Society published a list of 2013-2014 doctoral degrees in mathematics from U.S. institutions. Selecting random names from this list and checking the obvious places for papers should give a good estimate for what percentage have written at least one paper by a year and a half after graduating.
Unfortunately, I don't see a good way to sample uniformly from this list, without some counting or approximations. Instead, I flipped through it and grabbed ten names from near the centers of the pages, about three pages apart (in a 31-page document). This isn't a particularly careful sampling technique, and it presumably introduced some bias, but it should suffice to detect anything occurring 90% of the time.
For each of the ten people I selected, I looked for mathematics papers on Google Scholar, the arXiv, a home page, or MathSciNet. I did not count the dissertation itself, and I was prepared to exclude anything that appeared to be undergraduate research but this turned out not to be an issue. The results were as follows:
Six people had publications in journals.
Two more had papers they described as accepted by journals.
One listed a conference publication. Web searches make it clear that this paper exists (and it has been cited by another paper with disjoint authors), but I could not find a copy online.
For the remaining person, I found no evidence of any papers.
I was surprised at how high the percentage of people with publications was, and perhaps it indicates that my sample was not so representative. However, it appears that even people working in teaching-only jobs or outside academia are likely to write at least one paper.
If anyone carries out a more careful study of this issue, I would love to see the results.