Whether or not the ship broke apart would have had no consequence with regard to insurance claims. The breakup was the result of what would have been a covered accident. So, insurance should have had little to do with the obvious coverup of the accurately-described breakup.
My best speculation is that Titanic was built to Harland & Wolff specifications which were "outside" the scantling tables for ships in 1912. Scantling tables were listings of the minimum sizes and weights of materials to be used in the construction of ships. These tables were published by "classification societies" which oversaw ship construction primarily on behalf of the insurance industry. A ship could only be insured if it met the applicable scantlings.
Oddly, those tables in 1912 ended at 620 feet overall length of hull. Even in those days the regulators were behind reality.
Harland & Wolff arguably had more experience building metal ships than any company in the world. This gave them an edge in knowing what size materials would and would not work. To White Star, this meant H&W could design a lighter weight ship of equivalent strength. That turned into cost savings, meaning higher profits over the life of the ship. These savings came from buying fewer tons of steel as well as from reducing the amount of fuel needed to cross the Atlantic. In ships as in cars, weight increases the amount of fuel needed to achieve any specified speed.
I seriously doubt H&W wanted the world to know that their new design might be in any way "flawed." No one could hold the builder responsible for running over an iceberg, but it one of its ships broke apart...well, that was another thing entirely. I can easily believe H&W actively campaigned to avoid discussion of the breakup.
White Star line had an equally vexing problem. Running over an iceberg was a peril of the sea. But, having one of their ships break apart would have been viewed quite differently by paying customers. Passengers might have shunned Olympic and the abuilding Britannic over fears the ships were under-built.
From the work I did on the TV documentaries "Titanic: Missing Pieces" and "Titanic" Achilles Heel," I can say that any fears over the H&W scantlings were unfounded. The ship's hull proved stronger than the design criteria. Lighter weight does not always mean a weaker ship and Titanic proved that. The ship broke apart because it was abused beyond the designers intent.
But, in 1912 the carcass of what had been Titanic was out of reach. Nobody could know what took place. And, while the calculations were well known, computing how and when the ship failed by hand (aided by "slipstick") was tedious and time consuming. It was simply best for all parties to avoid the subject of the breakup. The coverup worked until the wreck was discovered in two pieces.
-- David G. Brown