In the interview with ExWeb, Burch says that it is his understanding that permits are not needed to climb any mountains under 5800 meters (19,028 feet). In fact, these mountains are categorized as "trekking peaks" so as to avoid a lot of unnecessary paperwork for travelers who come to Nepal and just want to hike in the Himalaya for a few weeks. Back in October, the American adventurer summited 31 different mountains there over the course of a three week period. But, according to him, all of them were under the 5800 meter mark, which meant he didn't need to obtain permits for his expedition.
To add further fuel to the fire, Burch also says that the reporter who wrote the initial story for The Himalayan Times didn't get all of the facts right. It was first reported that he had climbed above 6500 meters (21,325 ft), which is the altitude at which a liaison officer is required. The original story also said that he claimed to have summited three mountains – Kangnun Himal, Chandi Himal, and Changla Himal – none of which he actually climbed. Burch says the highest altitude that he reached during his expedition was 5793 meters (19,006 ft), and that everything he did followed the rules and regulations. The initial story even says that he lives and works in Nepal, which apparently isn't true either.
It is difficult to say exactly where these stories started, but if it is true that Burch never ventured above 5800 meters, than he is correct in saying that he didn't need a permit. It seems likely that all of this will be sorted out by the Nepali government in good time, but it has made for splashy headlines in the mountaineering community in recent weeks. The American isn't the only to fall into this category either, as a team of Spanish climbers has also been accused of not having the proper permits as well.
At this point, the stories seems to have been blown well out of proportion, and it appears that Burch hasn't done anything wrong. Hopefully this will all get sorted out and blow over soon.