One way in which corruption is directly involved in this is that the Ministry of Religious Affairs is a patronage post, but it has a lot of power over some of the ordinary administrative decisions that would impact a religious community, like permission to build a church, permission to expand a church, things like that.
The religious affairs ministry is a patronage post that was handed out by the president to somebody who is a radical extremist Sunni Muslim. Then, to make matters worse, there are all kinds of suggestions of corruption within that ministry, which, among other things, oversees the hajj to Saudi Arabia. That is a complicated thing, but basically the government helps Indonesians travel to Saudi Arabia, and bankrolls some of them, and there is a trust fund for others; there is a lot of money at stake. There is a lot of corruption in that ministry, and having it presumably puts a person in a place where they can actually reap some of the rewards, so to speak. That's one way it's directly involved in this.
On a general level, all I'd say about corruption is that it's just one more piece of evidence about the arbitrariness of the legal system, that if a radical extremist group attacks a Christian mosque, you can be pretty sure they're also going to have enough money to bribe the police to avoid prosecution afterwards.