Myth: Lacking refrigeration, medieval people had no way to preserve food, and so when meat went rotten (as it so frequently did), spices were used to disguise the taste.
Fact: Medieval people usually cooked and ate their meat within a few days of the animal's slaughter or death in the hunt, and, depending on the type of meat, often the same day. This is actually fresher than the meat consumed by most people in the U.S. today.
It's true that people in the Middle Ages had no refrigeration aside from that provided naturally by cold weather; but when there was a need to preserve meat, there were several commonly-known ways to do so, including drying, smoking, soaking in brine and packing in salt.
Spices were much too expensive to waste on bad meat, and no amount of spices can really disguise the taste of truly rotten meat -- which, unless you have long been accustomed to it -- will make you sick.
And no, medieval people were not generally accustomed to rotten meat.
Origins of the Myth
The earliest reference to medieval people spicing rotten meat to hide its taste appears to be The Englishman's Food: Five Centuries of English Diet, by J. C. Drummond, first published in 1939. Drummond was not a historian, but a professor of biochemistry. He made no claims to expertise in either medieval life or food history; however, in his book he made several statements about medieval food preparation as if they had long been accepted as fact, when in reality there was, and is, no evidence to substantiate them.