Am too a non-statistician. If I understand correctly: The two groups have very strong statistical relations across multiple variables (not just COPD), yet the s

Am too a non-statistician. If I understand correctly: The two groups have very strong statistical relations across multiple variables (not just COPD), yet the study clearly states they were chosen almost randomly. This is extremly unlikely to happen in a perfectly randomized test. What you describe is selecting the group in advance so they match (though you use only one variable). There are cases where doing this selection is reasonable and is useful. However, the study describes a different selection process. If the selection process described was not the one actually used, what else in the study does not match reality?