"What he's dealing with" involves more than just the rumors. He's probably most concerned about what *legal* issues may be involved, and since the investigators haven't contacted him, he has no way of knowing what they might charge him with, if anything, and what evidence (circumstantial or otherwise) they may have.
For example, a seemingly unimportant piece of evidence or testimony from the maid might suddenly look incriminating if Rush says something that makes it *seem* to have significance, even if it's meaningless.
You just never know what piece of information from you or offhand comment might give your opponents ammunition against you.
Every legal advice book I've ever read says the same thing: If you are ever charged with a crime, or think you might be, SHUT UP. Any small thing you say might end up being the key thing that makes you *look* guilty, even if you aren't.
Consider, for example, any of the strident political attacks on conservatives. More often than not, they're based on some ridiculously trivial item or quote that can be spun into an overblown case that *sounds* plausible to the sheep. Who ever thought that Bush's minor comment about the British believing that Saddam was looking for uranium could be blown into a massive "Bush lied, the whole Iraq case was a sham" scandal?
You never know what might be used against you in court, so SHUT UP until you know everything you possibly can about what they think their case against you is, and what charges you're going to have to defend against.