SOCHI, Russia—Rooms without doorknobs, locks or heat, dysfunctional toilets, surprise early-morning fire alarms and packs of stray dogs: These are the initial images of the 2014 Winter Olympics that foreign journalists have blasted around the world from their officially assigned hotels—and the wave of criticism has rankled Russian officials.

Dmitry Kozak, the deputy prime minister responsible for the Olympic preparations, seemed to reflect the view held among many Russian officials that some Western visitors are deliberately...