Shlomo Sternberg (math professor at Harvard) wrote a book called "Group theory and physics". On p156 (link) there's a strange offhand comment:
"Experiments done in 1964 by Fitch and Cronin seem to indicate that CP is not conserved. I do not fully understand the issues involved in the correct interpretation of this experiment, which clearly shows that CP and CPT are not both conserved. It follows from the locality axioms, that quantum field theory implies that CPT is a symmetry of nature, and hence that CP is violated in the Fitch-Cronin experiment. But other, group theoretical, hypotheses might favor CP. I have my own views on the subject, which I will not expand on in this book."
I cannot find any other publication where Prof. Sternberg elaborated his views on this. But he obviously suspects that CP is an exact symmetry while CPT is not.
So the question is: (1) Does the Fitch-Cronin experiment (or any other) disprove CP? Or does it only "show that CP and CPT are not both conserved"? (2) If the latter, is it remotely plausible that CPT is false? (How universal is the CPT theorem? Does it hold even in string theory?)