No, the Koch's interest in criminal reform for the sake of the greater good is not "provably false". The Intercept article you posted is full of circumstantial evidence and rhetoric, and contains nothing that would be regarded as "proof". The strongest points it makes are:

1) The Kochs' money goes toward Republican candidates who oppose criminal reform.

2) The Kochs' interest was "sparked by the company's own environmental crimes"

Point 1 is as convincing as arguing that the ACLU and other liberals are also anti-criminal-reform, given that the majority of them likely voted for Bill and Hillary Clinton, despite the former being the president who advocated and signed America's most punitive federal sentencing reforms. The Koch brothers support conservatives, and some/many conservatives don't support or prioritize criminal reform. Also, you mischaracterize their political ad efforts. Their money goes to Republicans who have the discretion to spend it on whatever they like, including tough-on-crime candidates and platforms. The Kochs are indeed an accomplice to whatever their supported candidates decide to do with the money. But if the Kochs just want conservatives to win and don't actually care about criminal reform, why would they be quitely spending millions directly to support the kind of criminal reform advocacy that undercuts the GOP's status quo?

Point 2 is supported by a link to this TIME article: http://time.com/3686797/charles-koch-criminal-justice/

And the TIME article does indeed assert the Kochs' interest in criminal justice reform dates back to when their company was charged with environmental crimes and fined. And the Kochs' general counsel is quoted as supporting that timeline and that non-altruistic origin story:

> The owners believed they had been victimized by overzealous prosecutors and unclear statutes. “Our view was if we, a large company with many resources, were treated this way, what’s happening to the average American?” Holden says.

And...so? I didn't say the Kochs' got into criminal reform out of altruism. The op-ed I linked to from Doug Deason clearly has Deason talking about his personal run-in with the law. What I'm claiming is that, however they were first interested, what they are advocating now is reform that affects millions of convicts who are nowhere near Kochs' strata of self-interest, which the TIME article details (and the Intercept ignores). What does lobbying for better legal counsel for low-income/indigent defendants, restoring rights to youthful non-violent offenders, and reducing mandatory prison sentences, have to do with protecting the Kochs from prosecution for white-collar crimes. If the Kochs wanted to mitigate their exposure to future prosecution, they could just focus on lobbying for corporate and environmental deregulation.

The New Yorker has a more thorough article about the Kochs' possible motives and potential Trojan horse [1]. It notes that a previous iteration of the criminal reform bill, passed by the Senate committee, the House Judiciary Committee added provisions that would "weaken the government's ability to prosecute an array of corporate crimes". The Kochs spokesperson told the New Yorker at the time that the Kochs supported stripping the white-collar-crime provisions if that meant the bill could be passed.

[1] https://www.newyorker.com/magazine/2016/01/25/new-koch