No they don't. They just have to show that it is a reasonable possibility. It is the prosecution's responsibility to come up with the evidence to show that it is not a reasonable explanation. The defense doesn't have to prove anything, it is the prosecution has to disprove the alternate explanation. If they can't, then there remains a reasonable doubt, and the jury must acquit.
The prosecution has already tried to do that. By bringing the grandfather in, they have made the claim that it is unreasonable to think that he knew about the death for a couple of weeks and didn't say anything about it.
The defense is certainly putting their cards on the table, in an all or nothing sort of way. They leave themselves little wiggle room for, "here are a few other things to think about."
It is the