It neither contradicts commons sense, nor basic economics.
In classic (micro) economics, every good can be represented by two curves: A supply curve and a demand curve, plotted against price for the good and amount sold. The point where the two curves intersect defines the natural market price for that good.
Now if some external event comes along to make that product more desirable (say there's a snowstorm coming, and you are selling snowshovels), what will happen is the whole demand curve shifts to the right. We say "demand has increased". This causes a shift of the intersection, such that more of the product gets sold at a higher price. There's a positive relation between prices and sales in this case.
Now, all else being equal, this will generally happen slowly across an entire economy if its population is growing. Thus (in the USA at least) we typically expect to see a positive relation between inflation (prices) and economic growth and employment (amount of goods being made and sold). If there's some kind of hiccup (eg: a recession), they will hiccup together.
However, if something instead comes along to make a product harder to supply, what will instead happen is that the supply line shifts back to the left. This causes a new intersection to occur at a higher price and a lower supply. When the supply side is impacted, the relation between prices and supply is inverse.
What happened during the 70's was that the supply of oil dropped drasticly. Since oil (in the form of transportation costs) is an input into practically every good sold, the supply curve of nearly every product was impacted. This caused both higher prices (inflation) and a lower production of goods (slow or no growth, unemployment, etc).
The effects weren't pleasant to live through (unless you were an oil producer), but nothing particularly mysterious was going on.