Probably overthinking this exchange in absence of an update, but here's a do-over of mine with other suggestions worked in. Get a look at my insertion of the murder insinuations.
"Your father made his mistakes in life, that's true, but he's dead now. God rest him. I spoke to him at the Flower Fair just last May, Arthur, and after a long discussion with him not far from this very spot, I truly felt that he was ready to change his ways, but we'll never know what he could have done with that second chance. We'll never know what errors he was ready to openly and publicly admit." Toss Arthur a meaningful glance. "He died suddenly and strangely, and before the week was out, your sister was unpacked in his old quarters with anticipatory haste. And that's where his life's tale has to end."
"It's true. He had flaws that he'll never redeem this side of Judgment Day now, but let's not dwell on the flaws of the dead. You know those flaws much better than I could recite to you, and that's an encouraging sign that they won't be repeated. I won't begrudge you a game chance to correct his errors as the new Count. I want to help you, because it's the right thing to do, Arthur. I still care about that consideration, you know. What is right still means something to me. You are the rightful heir, and this is your patrimony at stake. If we don't press it now, we lose the moment."
"That loss would be a shame, for I think we share a rather unique perspective, you and I. We both know how it is to be viewed as common. I think that knowledge will assist your rule and give you the drive to prove them all wrong in the same way that it has done me. Thus for the right of the law, and for the good of the land and its people, I ask to advance your claim as the true Count Foles of Folesden."
I think we need to tell him the truth. Soon-to-be-Count Owen isn't exactly what we want as a neighbour. He probably knows why.
He's a fifteen year old bastard, not a courtier, and even
they probably don't know the depth of the rivalry. Owen is from a different county.
Will Arthur still be grateful if we were honest? Yeah, but not as much as to a supporter selflessly in his cause who doesn't equally need him on a practical level. This is simple basics of bargaining. Let him find out our other motives himself if he truly cares. Even their later discovery won't change much. Just a little "aha!" and a slight shrug by the time he finds out. We're under no obligation to disclose everything. Every man has his secret motivations.
Just why are we so sure hes the right claimant?
How do we know he's the right claimant? Because he's our claimant, and because we have the means to persuade others that he's the right claimant. Notice how the whore is useless dead weight? That's because the truth doesn't matter at this level of politics. Although if the money payments are real, he clearly has a valid claim.