Whether deserved or not, Bill Clinton’s USSS code name was “Eagle”. The “eagle on ice” is supposed tp depict that Billy Jeff is pining for the fjords, and is “on ice” until a State Funeral can be arranged - or a contrived time of announcement - timed for maximum negative impact on Trump, or Trump’s plan to disrupt Slow-Joe’s theft of the election.
The only way that works is if there’s any way that Trumps team could be left in the dark about it. And if the “rumor” is out there it’s been mentioned in some electronic form that’s intercept-able. If BC was dead, and being a Bernie for future use, it seems like the easy good guys countermove would just be to off the cuff mention condolences.