Actually it can be done with a little RF theory.
The way these things is by multiplying the incoming RF by a carrier of frequency very close to the radar frequency. The result is a lower-frequency product that can be sampled or simply compared in the analog domain to a reference. In this setup, the frequency we are multiplying by (the "LO" or "local oscillator") is what is detected remotely, because, as you point out, it has a very direct connection to the antenna.
Here's how you get around it:
Multiply by the expected radar frequency plus, say, 200 MHz. Before the multiplication, near the antenna jack, filter for radar frequency +/- 10 MHz (bandpass). Now the result of the multiplication will be very low-level signal except for a portion around f+/-10 MHz. You then sample this data. As you can see, the bandpass filter doesn't allow the LO to escape through the antenna connection.
Traditional receivers wouldn't do this because it wastes a lot of potentially useful bandwidth, but you can do this to avoid having the LO detected. Without much background on speed radar, I don't know how much variance there is in radar guns, but you would need to take this into account when designing the input filter and choosing the offset from expected frequency for the LO.
Not in textbooks, but definitely something that can be done.