Seems to me it's the opposite. For example if I'm making up a live service drop, I would cut the messenger and tie it out of the way first, then cut the hits. To reconnect, I would do the hots first then the messenger.
Perhaps the notion seems odd to you but consider the following.
When a person touches a hot wire with one hand and has one foot grounded, a path for current flow is established through the body. The amount of time and current passing through the body is limited by voltage (potential difference) and the resistance of the body. Other than wearing rubber gloves or other insulating materials there's not much we can do to increase the resistance of the human body.
Therefore, to protect against electric shock, one must consider the other two variables:
1. Reduce the voltage (potential difference) as much as possible. By reducing voltage less current will flow and therefore less damage is done to the human body. Stand guard because voltage to ground is ready to push current through the body.
2. Reduce the current as much as possible. We know that the flow of current through the body is what does the damage. Indeed, experts say that less than one amp could cause the heart to fibrillate.
Connecting the neutrals first works towards both of these goals:
1. Eliminates pressure to ground (nothing to push current through the body) because two points are maintained at the same potential.
2. Builds a low opposition path for current flow. In other words, it gives a path for current flow other than through the body.
The underlying assumption of the referenced scenario is that a bonding jumper exists if working in a metal box and the equipment grounding conductor is installed.
Similarly, what happens in a motor ground fault that is not bonded or grounded to anything and a person touched the case and a grounded material? What happens in a motor ground fault when a bonding jumper connects an equipment grounding conductor? Was something done about the voltage? Was something done about the current?
It's about reducing risks.