G'day, Lili-Marlene!
Thanks for finding the copy of the Merchant Shipping Act. I've saved it for reference.
Now let's see if I can explain the legal situation. What you have seems to be a muddled account that combines things from the British inquiry and the US court.
In Britain, the relevant section of the ACT is 503. This does not prevent anybody suing ship owners. What it does is limit the liability of of owners for losses of life or property in cases where there has been negligence by the owner's servants, without the 'knowledge or privity' of the owners. For instance, if a captain were to steer a dangerous course down a narrow channel in order to save time and fuel, without the knowledge and approval of the owner, then if the ship was wrecked the owner's liability was limited to £15 per Gross Registered Ton in the case of loss of life or injury. For loss of property it was £8 per ton. If a captain did something dangerous because he was ordered to, liability was unlimited. 'Knowledge or privity' was hard to prove. Dangerous instructions were not put in writing. (There's a poem about that, if I can find it).
In the case of Titanic, the ship was so big that White Star's liability was limited to about one million pounds. In the British Court of King's Bench the question of 'knowledge or privity' was never argued. Claimants simply claimed negligent navigation. The jury found that the navigation was negligent, because the speed of the ship was excessive, given the crew's knowledge of ice ahead. White Star tried to avoid paying by citing the conditions printed on the back of the contract tickets. These said that White Star accepted no liability for any kind of mishap. The presiding judge found the conditions were invalid, because the tickets were not in a form approved by the Board of Trade, a required by regulations under the Act. White Star appealed to a higher court, but lost again. An appeal to the Law Lords was considered, but it was dropped.
There seems to be no record of British claims settled out of court after the court cases. They may have been destroyed when White Star and Cunard combined.
In the USA, 'knowledge and privity' was at the heart of the civil claims. This was because US law limited damages to the salvage value of the ship, plus the freight moneys for the voyage. In Titanic's case, this amounted to about $96,000. In the US court, desperate attempts were therefore made to show that liability was unlimited. It was claimed that Bruce Ismay had urged Captain Smith to speed and that he had 'practically been allowed to captain the ship'. Witnesses distorted the truth considerably. In the end, the case was settled by an agreement that saw about a quarter of the damages claimed paid out, with no admission of liability. Claimants undertook to make no further claims.
The civil claims are quite well documented, though some of the US evidence is missing. I have a US document from 1917 in which a judge complains of incomplete records as early as that. Some more material may yet show up. An American friend tells me that US federal documents get stored in odd places, often miles from where they were originally produced.