Did the Supreme Court Approve the Order to Lock and Unload?

While researching my column about the District of Columbia's new gun law, I came across a tendentious assertion by Peter Nickles, D.C.'s acting attorney general, that I didn't have space to address. Defending the District's requirement that guns be kept both locked and unloaded until the very moment they're needed "to protect against a reasonably perceived threat of immediate harm to a person," Nickles told Washington Post columnist Marc Fisher:

It's clear the Supreme Court didn't intend for you to have a loaded gun around the house. I don't think the court thought this was going to become a Wild West scene.

Leaving aside Nickles' assumption that keeping a loaded gun in the house inexorably leads to "a Wild West scene" (a scenario that has not materialized even in juridictions where people are permitted to walk around in public with loaded guns), where, exactly, did the Supreme Court make it clear that keeping a loaded gun is beyond the protection of the Second Amendment? The majority opinion in D.C. v. Heller acknowledges that some forms of gun control are consistent with the Second Amendment and implies that they include "laws regulating the storage of firearms to prevent accidents." But that does not mean any law with that ostensible aim is valid; in fact, the Court found that D.C.'s law "regulating the storage of firearms" was unconstitutional because it effectively prevented people from using guns for self-defense. It did not explicitly address the constitutionality of a "safe storage" rule like the one the District has now adopted, which impedes self-defense and is more restrictive than necessary to prevent accidents (a goal that could be served by requiring, for example, that loaded firearms be kept in gun safes with their safeties on). But it's hard to see how the new rule can pass muster, since it substantially impinges on a gun owner's ability to defend himself while doing nothing to advance a legitimate government interest that could not be accomplished through less restrictive means.