On the matter of "Whether Falcone was telling the truth". . .
My own take is that Falcone *probably* was telling at least most of the truth. Unless Falcone was remarkably incompetent, Thomas Wayne wouldn't have any actual evidence implicating Falcone, just his word against Falcone. . . and his confession would *absolutely* incriminate himself more than it would prove anything against Falcone. Gotham City was at least mostly as corrupt then as in the present, and Falcone was already the dominant crime boss, so from Falcone's perspective, an accusation without evidence wouldn't be an immediate existential threat. Why take the risk of assassinating the richest man in the city when you can probably make the problem disappear via bribes and corruption within the police and DA office?
Basically, it makes more sense given the situation that Maroni would take the risky as hell move of assassinating a billionaire, comparatively speaking. Which doesn't mean its impossible that Falcone arranged it, or even that it was a completely random act of meaningless street crime. Note that part of "at least most of the truth" includes the option that Falcone *knows* Maroni wasn't behind it, and blames him anyway because its easy and useful. Falcone may not have murdered the Waynes, but that doesn't mean he wouldn't want to pull Bruce into his orbit if given the chance.
( Note that the one secret Falcone absolutely doesn't want getting out, and is willing to kill quickly to cover up, has nothing to do with the Waynes or murdering reporters or anything conventionally corrupt and criminal. It has to do with his secretly turning informant for the cops to eliminate his rival Maroni, which as demonstrated in the movie, is something which would destroy his own authority over the criminal underworld, no "beyond a reasonable doubt" needed. He's not afraid of being known as a murderous ruthless crime lord, or even as the secret ruler of the city; he's only afraid of his own subordinates viewing him as a traitor. )