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.
Then why hasn't Rush said so?
BRILLIANT idea!!! No sense VOLUNTEERING info that they can ADD TO some OTHER charge.