This case isn't remotely simple.
IIRC, Aylesbury gave money to the company without a tender, without checking for competition, and with competition in the area. And the council owns part of the company, and it is run by some councillors (I'm more vague on the latter part, though).
If the EU find the everything was done in a fair and above-board manner here, I'll eat Paddy Ashdown's hat.
However, the "competition" here was mainly wireless, which was somewhat ignored in the early stages of BDUK. Aylesbury might be able to argue that their behaviour was allowed by the earliest BDUK statements.
So the EU can give money to projects. But a government is banned from giving money?
Nope. Governments are allowed to give money ... but they have to persuade the EU that it isn't trampling over a competitive market when it does so, and that the money is handed out in a well-controlled manner. Simple ideas for fairness (but not simple to prove).
In the case of BDUK: Government wanted to give money; EU approved it with restrictions; Government agreed restrictions, and gave money; EU also gave money to a few projects too, mostly to cover SME in rural areas.
From the story, and the complaint, it appears that Aylesbury didn't follow the restrictions.