Hello,
I think that in the first part of the transmission they block each other out.
The controler gives a heading, followed by a beep and then the you can hear cactus 1549.
So it is possible that he did call a MAYDAY. This is consistent with previous reports from NTSB that a mayday was heard on the flightrecorder.
Talking from my own experience now. When you are in a emergency situation, one tents to forget to listen out on the frequency before making a call. I am not sure that it is the case now, but it is a possibility.
In my case, the first part of my transmission was blocked out by another aircraft. To be more accurate, I blocked out the other aircraft. At that time I didn't have any bits left to notice that the controler didn't read it back. I have learned from that, but I can't promise it will not happen again if I ever end up in the same situation.
I do not agree that a MAYDAY or PAN call is not important, because it is.
Specially in Europe procedures for ATC are based on those calls. A lot of things happen when such calls are being made. A lot of thing also happen when they are not made, but than the decision is made by somebody else and not on your flightdeck. And you can judge the best how bad your situation is.
Rgds
Martijn