Rush would have to be an idiot to say anything specific at this point.
Why is that? How does a flat denial hurt an innocent man?
I was with an innocent man when he went through interrogation because of a baseless claim by his wife. I told him to tell the truth and all would be well. Dumbest advice I have ever given. If I were ever asked to tell the police the truth about something, I would tell them forget it and I want a lawyer present before I think of speaking. ( I eventually got him off but only after several court appearances.)
In this case, a flat denial of what? Anything you say at this point will be disected and compared to whatever the police have. Learn what they have before you speak. I am sure that is what the lawyer has advised. In a situation like this, your only friend is your lawyer. Listen to them.