this is wrong at least for UNOS (united network for organ sharing)-which is the main system in the article-the current computer program used to find matches is an integer linear program. I think it is an interesting question if some kind of rule based system could replicate their ability to find the matches. I tend to think not.
https://pdfs.semanticscholar.org/0837/80a157a7f8ebfa44dce0bc...
page 16 "To our knowledge, there is no solver that would scale to the nationwide steady-state size— including the CMU solver used by UNOS. This solver is based on the work of Abraham et al. (2007), with enhancements and generalizations by Dickerson and Sandholm, and uses integer linear programming (IP) with one decision variable for each cycle no longer than L (in practice, L = 3) and constraints that state that accepted cycles are vertex disjoint. With specialized branch-andprice IP solving techniques, Abraham et al. (2007) were able to solve the (3-cycle, no chains, deterministic) problem at the projected steady-state nationwide scale of 10,000 patients"
edit: wait wait this comment could be out of date. The google scholar for this paper says 2018 but the paper says 2013??