They ran the tests on his elbow, because Beckett, not the Sox, was concerned about tingling in his arm. The Sox Doctors had cleared him to pitch. They tested his elbow, because that was his concern, not the shoulder. Beckett has had no shoulder concerns since 2000. He has missed no time with shoulder issues of any sort in his four years with the Red Sox.
http://fullcount.weei.com/sports/boston/baseball/red-sox/2010/02/09/the-importance-of-josh-becketts-shoulder/
So, he has had no problem with his shoulder in many years and he has a clean bill of health on his elbow as well.