A tire with an unknown history, even if it looks new, could have been subject to over or under-inflation, driven overloaded, been subjected to weather extremes, or repaired. These can all cause internal damage that is not readily visible. The components of a tire also break down over time, so that 'new' tire that's been sitting in somebody's stockroom for three years is no deal, and neither is the tire that’s ‘new’ but spent many years as a spare in a hot trunk.
With tires for some vehicles being very expensive, a used or remanufactured option looks tempting. In reality, that used tire is not a good deal when it compromises the safety of your vehicle. As the only contact between you and the road, your tires play the leading role in your car’s ability to start, maneuver, and stop. Invest in quality. Even if your driving is usually at moderate speeds and relatively light loads, an occasional high speed trip loaded with passengers and luggage will more than justify having the best you can afford. And, with proper care, the better tire will perform and wear better.