Why do you think Dansforth is concerned whether Proctor has told anyone else about the girls' lies?
Danforth is no idiot. He is aware that around Salem township, other courts have dealt with similar issues. These towns are not all finding conviction in the people they put on trial like Salem currently experiences. In fact, their courts are coming to the conclusion that many of these people being accused of witchery are really not witches at all. I am confident that Danforth would worry that Proctor's claim might get out to other villages and they could come to the defense of Proctor in mass numbers.
Besides, Proctor has already gathered a strong delegation of the most religiously strong characters against the court. Danforth fears a rebellion. He also fears the loss of Hale who already seems to be wavering by this point.