RMS Titanic was never officially described as "unsinkable", that was only done by the gutter press. She was however described by White Star as "practically unsinkable", not quite the same.
My paternal grandfather had been working in a bank in Canada (where he was required to sleep with a loaded revolver under his pillow) but was returning to the UK to offer for the Methodist Ministry. He used to get up early and take a turn around the deck for exercise. One day he noticed that the sun was rising in the wrong place and asked one of the crew if the ship had turned around. The crewman asked him not to say anything to the other passengers until after breakfast but the ship was racing to the aid of the Titanic. She was released from assisting later that day and resumed her voyage.
My maternal grandparents married in April 1912. As was the custom those days pieces of wedding cake were sent to relatives in Canada. They never received them and it was some time later that it dawned on my grandparents that of course the RMS Titanic was of course carrying the mails. I hope the crabs enjoyed a nice bit of cake!