
Unfortunately, you're wrong on both counts.  The most common method of
implementing a tunable receiver is to have a local oscillator.  The
local oscillator's frequency can be radiated out of the receiver via
the antenna unless the circuit is designed and constructed with great
care.

For a reference on detecting radios, get the paperback book _Spy Catcher_.
The author discovered how to detect radio receivers from their local
oscillator emissions back in the *1950s* while he worked for British
Intelligence.

  -Greg