I was beginning to dispair of finding intelligent life on this thread. Then I came to your post.
Actually, the Executive Branch DOES have a role to play in Judicial Branch decisions. The Solicitor General is there for the purpose of presenting the Administration's position to the Supreme Court. Where the government is a party to the case, the SG must take part in the case.
The second alternative comes in cases where the government is NOT a party. Then, the SG can come in if he and the President want to do that. The last and rarest opportunity is when the SG has not come in, and the Court INVITES a brief from the government. Though this is only a "request," any lawyer ignores a "request" from a judge at his peril.
No matter how the SG comes into a case, the Court always gives great weight to briefs filed by the SG. However, the Court is in no way bound to accept the postion set forth by the SG.
So it is a subtle role, and not a controlling role, but the Executive does have input in the course of Judicial decisions.
Congressman Billybob