Does that mean the frame picks up the 50Hz noise through the air?

Yes, your floating metallic structure is a source of 50 Hz due to capacitive coupling to 50 Hz cables and this structure can source current if grounded.

Single ended inputs use a ground wire and an input wire. The 50 Hz from the structure coupling forces a current to ground through the grounded wire and will generate (due to Faraday's law of induction) an interference voltage on the closely coupled input wire. So you get signal + interference.

If you used a balanced input, the noise would appear identically on both balanced inputs and would become theoretically zero at the input amplifier's output node (due to cancellation). This is because balanced inputs have the same impedance to ground and behave identically when an interfering signal is present.

Does that mean the frame picks up the 50Hz noise through the air?

Yes, your floating metallic structure is a source of 50 Hz due to capacitive coupling to 50 Hz cables and this structure can source current if grounded.

Single ended inputs use a ground wire and an input wire. The 50 Hz from the structure coupling forces a current to ground through the grounded wire and will generate (due to Faraday's law of induction) an interference voltage on the closely coupled input wire. So you get signal + interference: -

If you used a balanced input, the noise would appear identically on both balanced inputs and would become theoretically zero at the input amplifier's output node (due to cancellation). This is because balanced inputs have the same impedance to ground and behave identically when an interfering signal is present.