Theodore Cleaver was involved in the infamous fiftieth attempt to make the Philadelphia Experiment in early 1968. The field generator was augmented with a confoundium mesh, which was a dreadful mistake that ended the experiments for good and resulted in a significant increase in CIA agents, who were sent out to deal with the unwanted side effects.
It appears that Theodore was flung back in time by something on the order of sixty to sixty-five years. The earliest solid evidence we have of his activities are military base records from 1909, which suggests that he must have arrived by at least 1908, because a different time period requires a fair bit of reacclimation.
He is listed on the crew of a naval destroyer, as a third shift helmsman, which was in the general area. It is believed that the destroyer was the closest vessel to the Titanic at the time that it stuck the iceberg, an in steaming hard to its rescue, the helmsman made an error in judgement that caused the destroyer to collide with the Titanic aport, just fore of amidships.
The Titanic would have survived the iceberg had Cleaver not unintentionally rammed it on the other side, severely compromising its structural integrity. Distress calls from the destroyer were intermingled with transmissions from the destroyer, and the big ship carried the navy ship to the bottom, the two hulls so entangled together as to be indistinguishable.
So, the statement is partially correct: the Titanic was sunk by
The Beaver. It is assumed that Theodore perished in those cold waters, but that much is uncertain. The destroyer did have lifeboats, and there were odd reports in late April of strangers coming ashore in Gander, Qaqortoq, even as far away as Galway and Sligo (improbable but not entirely inconceivable), so what actually happened to the Beaver is uncertain, but he almost certainly did not sire his father.