Your dad is probably correct as to the original meaning when it was first used in the 60's. The government made the auto makers start marking their major components(block,trans, body, frame,...) with a partial vin so as to control car theft and chop shops easier.
By the 80's, the term had come to mean an original or restored car that still retained its original stamped major components, and car buyers were willing to pay a premium for a "matching numbers car"). Concourse type restorations even take the :numbers matching) to the next level, by making sure they use the correct part numbered intakes, carbs, distributors, etc., with a correct build date stamping
Unfortunately, when something drives the price of something upwards, there are people who will represent things to be what they are not. Lots of restamped carbs and distributors on the Internet.
If someone is selling a numbers matching car, they should be able to visually prove it to the buyer, and the buyer should confirm it.