"If an antenna can transmit, it can usually receive as just as well"
Yes, it's true; it's known as the principle of reciprocity.

The thing you're missing is that all other things must be equal. This includes the transmitter power, receiver sensitivity, noise and interference levels, etc.

In the case of your inductive loop, the large transmitting coil is much better at picking up the ambient 60 Hz field than the small receiving coil is, so when you use the transmitting coil as a receiver, the signal to noise ratio is vastly different.

In the case of your repeater, your transmit power is significantly less than that of the repeater, while the receiver sensitivities are probably very similar. Therefore, you can hear it even if it can't hear you.