IIRC: Olympic couldn’t be insured as it was involved in a collision with HMS Hawkeye; and was found at fault by the Royal Navy. There was also damage that couldn’t really be repaired resulting in an permanent slight port list and it was a floating legal liability. Titanic was insured for double its worth after this and White Star was owned by noted scumbag JP Morgan. Olympic was also being repaired at the same shipyard Titanic was being built at, making a switch that much easier.

My opinion: They swapped the boats in the yard to pass regulatory inspection for Olympic, then swapped back if there’s any truth to this.