Oh, the story I've read is it began in New England after the Blizzard of '78 when the major highways around Boston and Providence were closed for several days...so the supermarkets that were open weren't getting deliveries. Route 128, the main "ring road" around Boston, I believe they towed 5,000 abandoned cars off the highway in order to start plowing it. Not many four wheel drives, SUV wasn't even a term, and tons of rear-wheel drive boats still on the road. Pavement technology was older, we weren't as liberal with de-icing chemicals before the storms, and our plow trucks tended to be a bit smaller than today's diesel and often tandem axle trucks.
This wasn't the 1940s anymore when folks lived on farms, or in cities where you could walk to the corner market and it wasn't as big of a logistical challenge to move goods from the railroad depot to the stores. So folks who didn't have more than a couple days of perishables on hand found themselves short a few days after the storm when their street was plowed out and they got down to the supermarket to find they hadn't gotten any deliveries yet.
I'm sure, like the putting out Halloween candy before Labor Day (folks buy it on sale, then forget where they put it, and buy more...), the stores and distributors love to goose up the bread and milk stories so they can get folks to clean out their inventory and knowing a lot of it will end up in French Toast at best.
Of course we're unlikely to see another combination of events like the Blizzard of '78 to create gridlock from a storm that was forecast to be modest at best just a few hours before the snow started falling.