Finite input impedance of voltmeters
Is it coming from the ADC?

The ADC never directly connects to the probe input wires directly. It will use a  buffer amplifier as intermediary and, there will also be a variable attenuator to select the different voltage ranges. The variable attenuator in conjunction with the buffer amplifier will produce the 10 MΩ input resistance seen at the probe terminals.
If it helps, here is the input selection stage of an old analogue meter (the AVO): -

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