Incorrect. In most setups, Bodyguard is more powerful than Doctor.
Protecting a player with a Doctor ability allows you to mildly confirm them, and they were probably pretty likely town anyway (otherwise the scum probably wouldn't kill them, and even if they did, you probably wouldn't predict the kill). Unless the protected player has a power role, or you manage to protect twice (gaining a mislynch), this has effectively zero use for town.
Successfully using a Bodyguard ability allows you to fully confirm
When balancing setups, I balance Bodyguard like a fraction of an Innocent Child (depending on how likely it is to hit). Meanwhile, the value of Doctor in of itself is based only on the chance that two kills are stopped and town gains a mislynch. (In both cases, other power roles can become more valuable due to the inclusion of protective roles in the setup; something like an unlimited Cop is much stronger if the setup also has a Doctor, but that's one of the main cases in which a Doctor is better than a Bodyguard.)