Hi Willen,
As Jim said in post #2: "There is no direct current path for the rectified signal through the diode." What he means is that, for the the diode to conduct direct current, the diode has to be forward biased, ie the voltage at the anode of the diode must exceed the voltage at its cathode by at least the forward voltage drop of the diode (which is typically 0.6V for silicon signal diodes and 0.33V for germanium ones). In the radio schematic, there is no dc voltage return path to ground from the diode's cathode. Hence the diode can never be forward biased, and can never conduct dc. All that it can conduct in the configuration shown, is a tiny amount of AM RF ac, due to the diode's intrinsic capacitance, typically < 20pF in signal diodes. AM demodulation via diodes works like this: the am rf signal goes through a forward biased diode, which only passes that part of the waveform greater than the forward voltage drop. With the diode positioned as shown in the schematic, but having a dc return path to ground, eg a 10k resistor to ground from the diode's cathode (Ignore the schematic from this point on and instead concentrate on the text of this current post), we end up with a amplitude modulated train of purely positive voltage rectangular waves, which is the upper, positive half of the original AM waveform, less the forward voltage drop. This is then passed to the top connection of a resistor and capacitor in parallel with each other. The other ends of the resistor and capacitor connect to ground. The top connection is also connected, via a dc blocking capacitor, to the input of the audio amp. The resistor/capacitor combo act as an integrator, squeezing together the modulated rectangular waves into a positive dc voltage with no gaps & with the same modulation as the original AM signal. But because it is a varying dc voltage, it can pass through the blocking capacitor. This passage will convert the varying modulation voltage, which was always positive, into an ac voltage (imagine the dc voltage being pushed down through the x-axis, so that half of it is above and half below this axis). We have achieved demodulation of the am signal, the ac voltage at the input to the audio amp, is the audio signal which was modulated onto the carrier at the transmitter. Whew!!