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Wireless control devices have been around for many years, such as the remote control for your television. A wireless computer keyboard or mouse works in a much more complicated manner, unlike TV remotes where you can sometimes use them to change channels on your neighbor's television. I think people's familiarity with TV and DVD remotes is what causes unfounded concern when dealing with wireless input devices.
When you install a wireless keyboard and mouse on a computer, that PC establishes a sort of relationship with the device. The term for this is 'pairing' and it works the same way you might connect a Bluetooth headset to your mobile phone. This is why you often need to press a small connect button on the bottom or side of the keyboard or mouse during the install process. Once you pair the wireless keyboard and mouse to your computer, this prevents other computers from recognizing it because those input devices are already in a relationship with your PC. In other words, wireless keyboards and mice make for faithful partners.
(Image credit: Wikimedia Commons)