Aside from a total lack of positive evidence, there are many problems with this theory, some of which have been noted:
- Photographs from the wreck show that the propellers bear Titanic's Harland & Wolff hull number (401), not Olympic's (400).
- Olympic and Titanic had subtle but significant structural differences. These included the enclosure of the A-Deck forward promenade, the Cafe Parisian on B-Deck for first class passengers, and the replacement of B-Deck's public promenade with cabins and two suites featuring private promenades. These changes (especially the last) were involved major structural redesigns, and it would have been very expensive to retrofit Olympic with them (and possibly remove them on Titanic, depending on when the scheme was launched).
- After the Titanic disaster, Olympic's double bottom was extended up to the waterline, requiring a lengthy and very costly dry-docking, and more importantly, major structural work in the very areas damaged by the Hawke. There seems little reason to swap ships and sink the Olympic when such substantial modifications followed the accident. Even an intentional (non-iceberg) sinking must have involved hull damage, and given the Olympic class' "unsinkable" reputation, White Star must have known that substantial refitting work would be required after the loss of one.
White Star did propose that the rescue ship Carpathia, which was en route to the Mediterranean and not provisioned for hundreds of extra passengers, rendezvous with the Olympic in mid-ocean and transfer the Titanic survivors to her. Needless to say, the survivors were not enthusiastic about boarding Titanic's nearly identical twin, so the Carpathia returned to New York.
Keynes is dead and we are living in his long run.