More importantly, there's a lot of background noise on HF bands that will mask that weak signal.
If you've never built a radio and tried to shield this unintended export than I can totally see how you might think this is just a matter of careful design and more shielding but it really is a lot harder than that and you will simply never reach zero to the point where even an ordinary spectrum analyzer hooked up to the input of your radio will not show the oscillator frequency as a nice fat peak.
I learned a lot during that project, especially how hard it is to make an oscillator that does not radiate. So, it got to the point where I could reliably detect the receiver from about 100 meters away, fortunately the counterparty never started out from the assumption that it would be in that particular location to begin with. Trawling for a signal is a lot harder than verifying that is is there. But if you know the modulation and the frequency the receiver uses for its mixing stage this is a very hard problem to solve in such a way that there is absolutely no power radiated out of the reception antenna. Any kind of magnetic or capacitive coupler is bi-directional. Maybe with today's hardware capabilities it would be possible to pull the whole thing into the digital domain at a very early stage and that way I can see a few options to make it 100% clean but in the analog domain I do not see a bullet proof way of achieving this.