Well the only human data is in figure 1, and it doesn't look that convincing. There seems to be a small difference in oxalate metabolism between people with/without coronary disease. They do a bunch of comparisons which aren't corrected for multiple testing, and then claim it is of some relevance which is the 'most significant' based on the lowest p.value. This is poor statistical practice if you ask me, such language should not be permitted in an academic paper, although this is utterly typical of nutritional science and life sciences in general. In any case, I think it is crazy to test the association between some nutritional/metabolic factor and a disease outcome in just 48 humans, the results are almost certainly bunk.

The translation is that in actual humans, oxalate metabolism possibly isn't that important to cardiovascular outcomes on average. But it is probably important for some people.