If you think that's what I mean, then you didn't get my point.
If you and I start with the same premises and end up at different conclusions, then we know that at least one of us is wrong. This doesn't imply that I'm right and you're wrong; it could be the other way around. Heck - we could both be wrong... but we couldn't both be right.
If there is one reality then two people can't have conflicting beliefs and both be right. Both may be wrong, but chances are one might be closer than the other and thus applying reason a little better.