Nah -- anyone who believes in the 'ship swap' conspiracy is seriously deficient in their analytical skills.
When I was at university I wrote a dissertation analysing/refuting the conspiracy theory. Forty-four pages devoted to proving Titanic sank -- the best grade I got! (SMILE) It's on my website (see the articles section).
I did look for some more information, Pedro, and Olympic made headlines in July-August 1924:
'"46,000 tons lifted forty feet; Strange Voyage of the Olympic; Dry Dock Feat; World Record Made in Silence," the special correspondent of the Daily Express wrote in a fine news story about the Olympic in the floating dock at Southampton. "The greatest weight-lifting feat in the world has been accomplished here."' Apparently it took three hours forty-five minutes to lift Olympic.
It uses the gross register tonnage, unfortunately, rather than the better displacement tonnage; it's also interesting that the reporter referred to it as a 'dry dock.' A better description would be 'floating dry-dock' or even 'floating dock' (both descriptions, and especially 'floating dry-dock' appear in period sources).
I'm not sure if this photo postcard dates from 1924, but it's certainly mid-1920s. It looks like it's pre-1929 from the appearance of Olympic's forward B-deck.
As a matter of interest we had 'Wooden' floating drydocks here in use on Tyneside in 1903, one local well known one was Winlo's dock.
Many of the larger steel floating drydocks were also built here also in the 1920's.
The drydock in the picture could be one built on the Tyne and there is a picture of it leaving the Tyne for Southampton in John H. Prouds '150 Years of the Maltese Cross' on page 186.