If two parties in dispute can’t agree on what it is they’re arguing about, a settlement is probably a long way off.

So it is with the row between Rwanda and, what seems to be the rest of the world, or at least its neighbor DR Congo, the UN, the US and a host of human rights groups monitoring the region. In fact in this dispute at least, Rwanda seems to be conspicuously alone in insisting that it is not involved in the most recent rebellion to plague Eastern Congo.

In April, a group of Congolese soldiers deserted their posts, loaded their weapons and retreated to a small group of mountaintops tucked into the corner where Congo meets Rwanda and Uganda. It was an audacious rebellion that challenged the authority of Kinshasa, and threatened to tip the already dangerously unstable region into open warfare.

Like so many of the issues in this corner of the Congo, the reasons behind it are complicated, multi-layered and not as they might first appear, but at the risk of over-simplifying things, it boils down to this: the rebels say they quit the army in a dispute over pay and conditions the Congolese government, the UN and human rights groups among others all accuse Rwanda of organizing and supplying the insurrection and Rwanda says the allegations are an outrageous attempt to smear it.

Rwanda’s president Paul Kagame has long been accused of meddling over the border, and there is a historical precedent. For years after the Rwandan Genocide of 1994 when hundreds of thousands of refugees fled into what was then Zaire, Kagame’s troops went in, hunting down those responsible for the killing, and supporting another insurgency friendly to Kigali that ultimately became the government.

But now, Kagame insists while he maintains an interest in what happens in Congo, he does not intervene.

I spoke to the Rwandan president shortly after the UN’s Monitoring Group on DR Congo issued a report that included an unprecedented level of detail about exactly how it believes Kigali is meddling. The report includes dates of meetings with Rwandan officials names of people who attended them photographs of ammunition it alleges could only have come from Rwanda even a map detailing how the rebels moved from their army base to their mountain redoubt through Rwandan territory.

On the face of it, it appears to be so well documented and so comprehensive that Kagame would have no choice but to admit his involvement.

But he is not a man who gives in. Period. He was in a combative mood when I met him at his office in Kigali. When I pressed him on the detail in the report, he jabbed the air with his finger and dismissed the document as “fiction”.

“There is no truth in it, because we are not involved,” he said. “I don’t know where these things come from but it is just not true.”

And he went on to complain that the report represents only the view from over the border.

“Nobody came to ask us about these allegations. Nobody. It was written behind our backs, as if it was a big secret.”

If they had a chance to talk to the investigators, the Rwandans say they would have made a point-by-point rebuttal of each of the allegations. (The Monitoring Group has agreed to meet Rwandan officials shortly, and include their response in an annex.)

But to Kagame’s eyes, Rwanda is being accused of meddling as a way of diverting attention from the abject failure of both the Congolese government trying to stabilize the east, and the international groups who are trying to help it.

He may have a point. Government is almost non-existent. A bewildering and appallingly dangerous medley of armed groups loot, rape and murder their way around the frontier provinces with complete impunity, and human rights groups usually include the Congolese army its self in that category.

But after years of deteriorating violence, until the latest uprising, things appeared to be gradually settling down. And Rwanda claimed some credit for that, arguing that it had worked hard to improve its relationship with Kinshasa and help resolve some of the problems in the east.

Which was also why Kagame said he was so exasperated by the latest allegations.

Whatever the truth of the matter, the rebellion has undone what little progress had been made in the past few years, and threatened to spin the violence into a wider war that could once again suck in neighbouring states.

But as long as Kinshasa and Kigali are arguing about why the rebellion happened in the first place, they are unlikely to agree on what to do about it.