It's possible that when you spin the wheel without a tire mounted, the brake track looks true, but if the tire is not symmetrical or bulges unevenly, once the tire is mounted, the spinning tire might look un-true (even though the brake track still looks true).

It's also possible that the rim is true but with uneven spoke tension, so once the tire is mounted and pumped up, the rim is "compressed" and goes un-true.