If the US Navy refused Ballard's Titanic search support

Would naval historiography change if the US Navy refused Robert Ballard permission to use Alvin and Jason in the search that found Titanic?

Not greatly; Ballard could approach another partner, though the refusal might expose capability limits and weaken later private interest in deep-ocean searches.

Ballard could seek help elsewhere rather than abandon the work, so the historical effect would be limited. A refusal might reveal perceived limits in American deep-submergence capability and reduce later enthusiasm among wealthy private sponsors. It would not erase the broader development of wreck discovery and underwater research.