I think you have your intepretation of the situation a bit off. Dak has a Latissimus Dorsi issue right now on his chest below his arm. Tommy John is your elbow. Recent practice videos show Dak throwing short passes to keep nimble. You can't throw at all without significant pain if you have a UCL ligament ( Tommy John) problem. Imagine trying to run with a significant strain of your ACL. The diagnosis right now is an LD strain so light work and rest is the protocol.
Refer to pics below for visual clarification.
Latissimus Dorsi.