Behavior of Jack:
Jack is the manager, he does have the authority to correct Samantha but it is also his responsibility to make Samantha comfortable. He could have explained the situation to her calmly and make her understand the problem.
Jack did fail to some extent but he could rectify the mistake by apologizing and providing Samantha a clear explanation about how she can improve her performance. If Samantha does go to the PR and reports Jack, both of them leave the problem unsolved indicating lack of proper communication.
A manager should be able to communicate well with their workers and make them see the benefits for the company and their personal interests and then invest their effort into better performance.