This assertion is strange for two reasons. First, since prices generally rise through time (we have modest rates of inflation, not deflation), most prices will be at record highs most of the time. In other words, it is likely that the price of tables, hair cuts, bread and most other goods and services are at or near record highs.
The other reason why the assertion is strange is that it does not appear to be true. The Bureau of Labor Statistics (BLS) price index for used cars actually shows that they are lower, in nominal terms, than they had been in the late 90s (the graph shows nominal prices).
It is possible that the measures followed by USA Today do not track the BLS data closely because BLS makes quality adjustments in comparing prices. For example, if a car comes with a better braking system or sound system than the prior year's model, this will be factored into the price. A straight price comparison of the newer car with the older car may show a price increase, but when a value is assigned to these improved features, it may turn out that the price has remained the same or even fallen.