Where's the confusion? He's basically saying i don't think you're my son but I can't prove it, so the law gives you certain rights. How could he ever prove it? They don't have DNA testing. That's why the theory is interesting but kind of wack imo--how do they reveal it on the show?
FWIW, I have the same issue with Jon's parentage. How does it come out? Who would believe Bran, a Stark, even if he proves his magical powers. Who would believe Meera's father, a Stark ally? At least with Jon there could be letters or something, as it was a love affair that started a war. Don't see how Tyrion's lineage could be proven either way at this point, since if the theory is correct his mother was sleeping with both a Lannister and a Targaryen.