The commonly accepted time frame of 37 seconds across 1,300 feet is contested by Samuel Halpern, who has produced a LOT of material on Titanic.

Here's an article by Samuel Halpern about this and here's a much shorter news article on it. The gist of it is First Officer Murdoch (who was in charge of the vessel at that time) hesitated when he had 60 seconds until contact because he was trying to judge if Titanic would pass by safely. Turning would cause the stern to be exposed to the iceberg and he would have to perform a complicated porting-around maneuver quickly to avoid a strike. That's ultimately what he was forced to do when he realized Titanic was going to hit it. Halpern argued that had he not hesitated for up to 30 seconds (justified by a near-collision with another vessel in 1903), Titanic would have been fine and what we know about the disaster came after that decision which was not disclosed. Likely because the public would have put their heads on a pike at that point.

However, even the notion that they performed a port round maneuver is contested. Some say the order was never made. Others say the order was given but not carried out. Even more others say it was given when Murdoch realized impact was inevitable and did it as an attempt to avoid too much damage. Some even say Titanic struck the iceberg because it was avoiding more icebergs.

In short, even with all the information we have compared to how much information there can be, it's more difficult than one would think to come to a universally accepted conclusion. It's one of the reasons I find it so fascinating.

As a note, Encyclopedia Titanica is not just some random internet message board. It's populated by people who have written and published books about her and even handled artifacts.