Could the following scenario be a possibility:
1. The McCann's lawyer contacted Amaral's lawyer to say that they (McCanns/plaintiff) would be open to consider any reasonable settlement offer if defendant would be so minded to make one.
2. Amaral's lawyer responded to say that his client is considering his offer, but they need time, so would plaintiff's lawyer please apply for a postponement of court proceedings so negotiations could take place.
3. McCann's lawyer (whose prerogative it is) duly made such application which was granted.
4. Negotiations between the parties ensued, but ultimately came to nothing as plaintiff found defendant's offer unacceptable, and defendant was unwilling to alter it.
As has been pointed out earlier, if the McCanns had really not wished to proceed with the case, they could simply have withdrawn their action. In any legal proceedings it is invariably better to reach a settlement rather than proceed to trial, so I think it is immaterial which side made the first approach towards a settlement. In this particular case it was not reached.
You certainly have talent to write "novels"....but I'm afraid you got it wrong.
Mr. Amaral never wanted an agreement out of court, in fact he has been waiting anxiously for the trial - that's why the answer was so quick.
And you can't just withdraw from a case, there are legal consequences and quite grave as it would be considered as abusing the legal system. Furthermore, although I didn't have a chance to confirm, but Amaral said on several occasions that he was contersuing and if so, even if Mr. and Mrs McCann wished to withdraw they would have to respond for Mr. Amaral's allegations.
By the way, in Portugal every judicial process (criminal or "civil") is under the "secrecy of law" but the Trial sessions are public (except when it involves children or very intimate/delicate matters) and that's why people were able to twit on the last trial.