With a good isolation amplifier between your antenna and local oscillator, you don't necessarily transmit much on the frequency you're listening to. (If you did, you'd interfere with other listeners.) Where you transmit also depends very much on the design of the radio you're using; it might be obvious to detect that a radio is being operated, but not detect what frequency it is tuned to.
And to be very pedantic, every conductive object in the universe plays some part in any antenna system.
But some high-end SDRs use ridiculously-high sampling rates (like 200MHz), in which case many applications don't even need to mix a local oscillator with the incoming RF. It's pretty amazing.
I never learned much about RF, so this question may be naive. Is it possible to sample higher frequency signals using a 200MHz sample rate, by using a bandpass filter and then deliberately undersampling without an anti-alias filter? If so, how high could you go, and what other limitations exist?
"BBC admits that TV detector vans only work because Britons believe they do"
http://gadgets.boingboing.net/2008/10/31/bbc-admits-that-tv-...