BBC is not proving anything here. It is news reporting in the article. They have given more details on their reporting. We can take it or leave it.

The statements seem odd on their own until you read the article. Here’s a bit of it:

1. Ties to right-wing extremist groups were few
Far-right insignia was spotted on the clothing, badges and flags of several insurrectionists, but the vast majority of the 200-plus people charged so far are ordinary pro-Trump activists.

So far, only about 10% of those charged have been found to have ties to organised far right militias or other right-wing extremist groups.

"What we are dealing with here is not merely a mix of right-wing organisations, but a broader mass movement with violence at its core," wrote Dr Robert Pape, director of the Chicago Project on Security & Threats.

Dr Pape led a 22-person research team from the University of Chicago in a study — titled “Faces of the American Insurrection” — that takes a closer look at who has been arrested since 6 January.

2. More rioters came from 'Biden counties' than 'Trump counties'
The mob was largely pro-Trump, but they came from all parts of the country.

The rioters facing federal charges hail from 41 out of the 50 US states and the District of Columbia, according to the George Washington University extremism tracker.

The University of Chicago report finds that most of the insurrectionists came from large urban counties where Joe Biden beat Donald Trump by slim-to-moderate margins in the 2020 election.

These counties typically contain big and racially diverse populations.

Only a few came from pro-Trump strongholds.

"This will come as a surprise to many Biden supporters, who presumably think that the insurrectionists are coming from red counties - rural, almost completely white, and with high unemployment - far from Biden strongholds," said Dr Pape.
"This is fundamentally a political movement, one not only centered in "red" parts of the country, but also consisting of pro-Trump supporters who are in the political minority in many places."