I had this same question.  If the transaction is never broadcast, then surely he can spend his coins, then the transaction is invalid when the grandson tries to cash it in.  If he broadcasts it right away, then it must somehow be revoked or modified for the death claim to work.  Is this understanding correct?  But that would still create a small window where the old tx is modified and the new contract added, leaving a chance for a spend in that time.  My understanding of txs is still very rudimentary, so I feel like I must be missing an important piece of this.