No they didn't make a Mayday. It is also unlikely that the scenarios put forward here occurred as the passenger accounts of what happened match the crew accounts. I think the crew would have understood their obligations under the TSI Act that they were legally required to provide all information with self-incrimination not being a defense against not telling the truth.
Also the F/O would not have had any reason to give an account that was not accurate. If they didn't tell the truth then I doubt that they will be looking forward to the Senate Enquiry. If I was the crew I wouldn't be looking forward to it anyway because I don't think that it will exonerate them if that is what they are after. The Senator's are not fools and they will soon realise that the accident could have been avoided if different decisions were made by the crew even after they realised that the weather was below minima and they didn't have the fuel for an alternate.
Remember the Mt Hotham accident? After the report was released there was all sorts of speculation that the ATSB had got it wrong and that it wasn't the pilots fault but a failed engine that caused them to hit the hill.A supplementary report released in response to the publicity showed that the pilot had flown a similar dodgy approach in the morning. End of speculation.