It also points to the engine room being dry until the break up because if the engine was getting flooded at around 01:40 Titanic time, the time at which Phillips sent the "Engine Room getting flooded" or "Engine Room full up to the boilers" message, the circuit breakers in the engine room would have all opened and any electrical supplies from them would have ended. This would include the main lighting.
Then why sent it out as the last distress? I tend to believe in a critical situation as that, they would say what they mean and mean what they say - the Engine Room was full up. If this wasn't the case, why not say, "Boiler Rooms flooding" (Again, that they didn't say this is why I hypothesize that the boiler rooms, were mostly dry, save for the forward most).
The only possibility to why they would lie would be to make the situation seem more critical than it was at that hour, and I don't believe they'd resort to that.