Your interpretation is wrong, unfortunately. The paper is really about developing a multi-marker sensor approach for screening. The analysis, however was done

Your interpretation is wrong, unfortunately. The paper is really about developing a multi-marker sensor approach for screening. The analysis, however was done on a small set "Obtained data from 76 urine specimens were partitioned randomly into a training data set (70% of total) and a test data set (30% of total). " Later on it states the 76 samples are from 51 individuals. So the GP complaint is correct in this case. They are comparing a RF approach and a NN approach - there isn't much detail in the paper but it's most likely the analysis is problematic. I suspect this was done because the group is a collection of hardware and clinical folks, not statisticians, and the paper would have benefited by review by a biostats person. You are quite right generally that for some models and some effects, a relatively small verification set can be effective.