the names on the Berlin manifest have a pencil line drawn through them
Names on the manifest were lined out when the passengers did not sail.
See Marian L. Smith's article A Guide to Interpreting Passenger List Annotations at JewishGen.org. The information you want is on the page Markings on the Manifest's Left Margin, under the section "Not Shipped," N.O.B., or "Did Not Sail":
Often passengers booked to sail on a given ship did not depart. Perhaps they missed the ship, or changed their travel plans, or became ill and health officials prevented them from boarding the ship. Whatever the case, in some instances the change or decision occurred so late there was no time to amend the passenger list. Their names and passenger information remain on lists for ships upon which they never arrived.
To indicate the record is meaningless, steamship company employees would mark the record in one of several ways. The most common was to "line out" the entire record with dark grease pencil or ink. Some of the lines are straight across and can be difficult to differentiate from scratches on the microfilm. Others are deliberately "wavy."
We can still glean useful information from these manifests, even if the passengers didn't sail. Imagine if the manifest for the Carpathia was unreadable -- you would have been able to retrieve much of the same information from the Berlin's passenger manifest.
Update: In March 2017, Marian L. Smith presented a live webinar at USCIS demonstrating how we can fail to find someone in the passenger lists because of common misconceptions. One of the common misconceptions is that the passengers were involved in the creation of the lists. Smith showed a copy of the forms that were given to passenger at the Cunard Line office with the questions that needed to be answered for the passenger lists. These forms were used in the steamship company offices to create the passenger lists -- and most of the pages in a passenger list would have been created before the ship left the departure port. (The exceptions would be any notations about births and deaths on board, which couldn't have been added until after the events had happened, and the pages for the passengers who had to appear before a Board of Special Inquiry.)
All the tickets were numbered. If passengers had to show their tickets as part of the boarding process, as we do when flying today, then the steamship company would know which passengers did not board.