The problem is, there is no direct proof. There is a ton of evidence.
That said, even the court of law, which is held to a MUCH higher burden on proof, can convict without 100% proof. Look at Hernandez. There is no video of him shooting Lloyd. But the other evidence makes a case that no reasonable person can defend.
In this case, there is no video of a needle entering a football. But there is plenty of evidence of wrongdoing. And the lack of a video suggests that the Pats deliberately concealed what they did, which is an admission of guilt. They didn't fully cooperate with the investigation, and still there is enough evidence to reasonably presume the Pats did it, with Brady at least knowing if not being more directly involved. And unlike the judicial system, there is no presumption of innocence. This is a private matter. The league can do whatever it wants.