I think we're all familiar with the background. Piraha is said to contradict the principles of universal grammar because it lacks embedding, but embedding and recursion aren't the same thing. Other forms of recursion exist. Does Piraha appear to have any?
I take the word "appear" literally, that is, it's a question about the evidence. Almost all of the publicly available evidence comes from Everett. You can consult the other works on listed Glottolog (please only consult those where it is probable that the author personally worked with speakers of the language); you can also consult Everett's thesis from 1983, which may reveal relevant data not generally discussed. Or you could start with Nevins, Pesetsky & Rodrigues (2009) 'Pirahã exceptionality: a reassessment' in Language 85, which will tell about the interepretation if not the data.