Following up on the other anon, Jon Arryn as you say as blind spots as wide as the Wall when it comes to seeing people's true character. If good!Joffery was sweet, dutiful, and basically the good future that Jon Arryn has been building towards since the Rebellion (Robert isn't Aerys but the Heir wants to come to Council Meetings!) would he be more suspect of Stannis and more blind to the blonde?
That’s a good point. Even someone significantly less credulous than Jon Arryn wouldn’t want to see it. The truth would be a stunning blow for something he worked so hard for, and one that comes back pretty harshly on his own judgment, as the person who insisted on the marriage.
And even if he did acknowledge it to himself, that’s not necessarily a guarantee that he’d do something about it. Coming forward would be a massive blow for a still very new regime, and what would it get him? A catastrophic hit to the regime’s credibility and an irreparable breach with Casterly Rock (because Tywin will never, ever admit it), so that he can replace a perfectly desirable and malleable young man with Stannis, who is widely unpopular and seems unlikely to have any sons of his own, guaranteeing another succession problem down the road. It’s only a problem if it gets out, after all. Maybe he quietly has Cersei poisoned to limit exposure and lets well enough alone.
Not that it matters for long, because he’ll either be shadowbabied for being an obstruction to Stannis or killed by little birds for getting in Aegon’s way, so. Perspective.