On what basis do you hold any such expectation? The paper explicitly contrasts its subject with several examples of convergent evolution producing functionally equivalent, but proteomically and genomically highly distinct, outcomes - which is typical of convergent evolution in general.
That said, I agree that the similarity of adjacent noncoding sequence is also a strong indicator that convergent evolution isn't causative here.
That said, I agree that the similarity of adjacent noncoding sequence is also a strong indicator that convergent evolution isn't causative here.