A hair-splitting nitpick: They couldn’t have sued for negligence, since that legal basis for claims for compensation in tort wasn’t recognised in English law until the seminal 1932 case of Donoghue v Stevenson. They would probably have sued on a contractual basis, with the additional twist that you would have to construe a contractual claim of those who died under contract which then passed on to their heirs by means of succession, since the relatives would, in most cases, not be in a contractual relationship with White Star themselves.
The title is based on the opening paragraph, which indicates that as the writer and his friends left the theatre after watching Titanic, his friends assumed that if it had happened today, there would have been many more lawsuits.
In essence, he’s simply rebutting the common assumption that people today are more litigious than they were a century ago, which simply isn’t the case; the Titanic litigation is a good example.