In the quiz following the segment, it stated that:
Audio sampling is: A digital recording of the sound
During the discussion within the segment, "a Strawberry Fields" sound was brought up. Was not the original Strawberry Fields keyboard intro sound recorded by the Beatles made with a Mellotron which was the first sample playback keyboard? The samples on the Mellotron were all analog tape I believe. This would make the recommended answer to the question above incorrect because audio sampling does not require the recorded sound to be digital.
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I guess this is another areas where semantics get mangled over time.
In digital signal theory, a sample is a discrete measurement of an analogue signal at a particular point in time, so an audio sample could be thought of as a sample of an audio signal at a particular point in time.
However a single sample is not much use, so a group of periodic samples is used to gather enough measurements to reconstruct an approximation of the original waveform. This is now generically termed an 'audio sample', which is really a segment or snippet of an audio waveform. Of course, using this terminology, it does not matter whether the audio segment is sourced from an analogue version or a digital version.