This reported e-mail, if it is correct at all, most likely was sent before HD dissappeared as part of their discussions about custody. For both parents, the non custodial parent would stand to lose a great deal financially if they didn't come to some sort of arrangement first. If it was left to the courts to decide, the non-custodial parent would lose the house for at least as long as the kids were there, plus they would have to pay support. Neither of them could afford to be the non custodial parent under those circumstances. The problem for CD is that with his criminal record and BDs lack of one, she would allmost certainly have been awarded custody if it was contested. On the other hand handing over title of house would have meant losing his only real asset. He probably wanted custody, but wasn't prepared to take the financial penalty for gaining it through negotiation or the risk of losing it by a court decision.
Most likely the outcome of those private negotiations was the status quo when HD dissappeared, in other words BD got custody and the house temporarily, while CD didn't have to pay support. It is a sort of compromise position between the two extremes.
It would be interesting to know who the source of that leak was. In theory only BD and CD would have known, but they might have discussed it with their families as well. I doubt that BD would have released that info since it makes her look bad, which means it must have been CD (or more probably someone in his family who wanted to inflame public feeling against BD and make her look bad).
Assuming it is true of course, it may simply be gossip or misinformation.