It's not that hard to make a positron source for that kind of experiment as you can just use some radioisotope that produces them by decay and you don't need a big accelerator.
Lots of scientists I've known tend to avoid radioisotopes, given either the inherent risks or the perceived risks. University bureaucracies can also create disincentives and barriers, even when the related procedures well known. The paper's paywalled for me, but I'd be interested to know what approach they took to generating the positrons and the beams.