unfortunately there's no coming back from what you said, because you showed that you asserted that the study was bullshit without actually reading it clearly. yes, you did not clearly read the study, your assertions about its content and/or conclusions are simply not consistent with its text. i can only conclude that you have an issue with krashen, or with applied linguistics, or are arguing in bad faith

a conclusion that something "does not inhibit" something else, and that it is "consistent" with other hypotheses, is simply not a causative conclusion, full stop

it is indeed true that correlations can tell you whether one thing inhibits another in the general sense. causatively? yes, if you have enough control data, which they do here (they controlled for class, gender, age, and location, which is enough to allow drawing negative-entailment causation from the correlation)