I didn't hear the version you mean, but took up my old fiddle and tried to slide all the way down from A to E on the E string. I found out that this is only possible with the index.
But I guess what Christian says is right: it SOUNDS like you slide all the way, but actually you only go down to somewhere around the G and then release the string. You hardly hear the difference. Matter of bowing/timing.
So you can use any finger for that. (wouldn't recommend the pinkie though)

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