A submarine was also out in the ocean, just in case the iceberg did not do the trick. Supposedly. Not sure if that bit was in the documentary you viewed.
A submarine was not mentioned in the documentary, but they did say that ships rarely hit icebergs. This is simply not true in the modern era:
There are no globally-collated figures for iceberg strikes, but they happen every year. For the northern hemisphere, from 1980 to 2005, there were 57 incidents involving icebergs giving a rate of 2.3 per year, according to Brian Hill, of the Institute for Ocean Technology, who maintains a database of more than 680 iceberg-ship incidents.
But I did find a "no-iceberger" that goes on the record.
Exploring the Possibility That the Titanic Was Sunk by a German U-Boat | Barstool Sports