TLDR: 60 volts AC divided by the transformer CMRR is much greater than 1 mA times the resistance of the wire installed.
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In the first case - the raspberry Pi was floating at 60 V AC above ground, being powered by a two-pin USB adapter. The radio was earthed by its power supply, coax, etc. So the transformers have 60 volts across them, and even the smallest asymmetry of capacitance will generate a large differential-mode signal.
In the second case, there's a maximum of (say) 1 mA flowing on the ground wire (there's a legal limit for leakage, something like that). A small voltage develops across this resistance, which is added to the audio signal. The transformers are probably still helping.
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Transformer isolation is much more important in cases like this:
Imagine you have a grounded computer plugged in on one end of the room, and a grounded rig plugged in on the other. Your air conditioner is causing a 1 volt drop in the ground/neutral potential between the two sockets, but this 1 volt is at a very low impedance. The simple sound-card earth wire is completely overwhelmed by this, and simply drops the 1 volt too, resulting in a 1 volt differential AC signal added to the audio at the rig/PC. In this case, the transformers provide a vital function, breaking the so-called ground loop.
In your first case, you have a high voltage, high impedance voltage difference between the two halves, so the right solution is a heavy ground wire. Then you use the transformer in the USB power supply for ground isolation.
