In my opinion, J.P. Morgan is not brought into the Titanic story because he had any direct influence on the events of that night. Rather, he is conjured up in an attempt to show how the rich robber barons were attempting to gain wealth at the expense of the poor and the downtrodden. This thinly disguised dialectic materialism is a major theme of most cinematic portrayals of the disaster even though it is historically innacurate.
J.P. Morgan had no direct interest in operating ships per se. His interests were financial, and particularly in the control of the flow of goods, people, and money. While he may have been behind the financing of Titanic, he was not in any practical sense the "owner." As has been pointed out, shares in companies controlled by Morgan were traded in public. The honor of ownership rested with the corporate body known as White Star, which effectively meant, Bruce Ismay. The ship was British from keel to truck, crewed British, and sailed under British regulations and flag. In fact, had a member of the U.S. Navy tried to take control of Titanic (or Olympic), it would technically have been an act of war against Great Britain. (A century earlier, the U.S. went to war against England for just those sorts of actions.)
The situation regarding the nationality of ships is still confusing. A vessel may be financed by people of one country, owned by a corporation of another, and flagged (registered) under the laws of yet a third country. And, to add to the confusion, the captain and crew may represent a dozen more nations.
The costs of operating ships under the U.S. flag are considerably greater than when operating under the flags of a lot of third countries. Thus, U.S. corporations often register their ships overseas to escape direct U.S. control and expense. This is called using a "flag of convenience."
Today there is even more international control of corporations than in 1912. The "owners" of a U.S. company may really be from still another nation state. Nothing is new. This is just ol' J.P. Morgan on a larger scale.
--David G. Brown