He's correct, which is why we backed off on kidnapping as a capital offense. Once you made the act of kidnapping a capital crime, the kidnapper had no reason at all to not kill the victim.
You overstate the case. The incentive not to kill the victim is reduced, but to say "no reason at all" is wrong.
In the case of rape, the probability of being convicted of rape+murder due to the extra police interest and evidence (dead body) is higher then being convicted of rape where there is no strong physical proof that a crime even occured (no dead body, he said she said, etc.)
Is this proof that the death Penalty is a deterent?