I just seems strange that they would market a ship as specifically not going to sink.
Sure safety is probably a selling point, but it just seems like that unsinkability was tacked on later.
It appears there were references to Titanic and her sister ship Olympic being "unsinkable" made in printed advertising by White Star Lines, in 1910, prior to either ship being in service. This article has a scan of such an advertisement as well as a discussion generally on the subject.
Controversially, the ship's builders, Harland and Wolff, claim they never made such a claim.