That should only be a problem on the first serve. Otherwise I'd tell my opponent that they're allowed to call their own shots out if it's that obvious. I don't know why they'd have a problem with you playing a ball that was out since it does nothing to hurt them. I certainly wouldn't replay the point - they admit to having hit the ball out.
Yes, it's on first serve. Should have been more clear.
2x BLX 6.1 Pro Staff 95: 12 oz., 8 pts. HL, SW 325
VS Touch Black/Focus Hex 1.23 @ 58/54