You absolutely can though. A 16x7 grid of light switches can store any 16 character password that uses the ASCII character set. Images would require many more switches (depending on the color quality and resolution) but it's the same thing. Like I said, earlier, you are having an issue making a point to differentiate between the position of a binary switch and a single bit of data because there is no fucking difference in the first place.

You make it sound ridiculous, but we've stored data as a magnetic polarity for decades at this point, we've stored data on rocks, laser etched as dots and dashes at a microscopic level on thin bits of foil. Whole programs have been written and stored on stacks of cards. Heck, the programs to get a spacecraft to the moon were written on paper and then literally knitted into the onboard computers. Regardless of the medium chosen, (almost) all computer memory and storage is simply the representation of an array of binary states, something that can be done, and has been done with a simple array of light switches.