I appreciate you finding that article - interesting one.

I'm very much amateur curler, and can't see how that tiny touch would impact it, but maybe it does at that level of competition.

Using a perfect shot to stop on the button with no spin, and energy= all kinetic (1/2mv2) =friction energy(F*deltaX), we get a release speed of 1.8m/s (with a .006 coefficient), and a 2.98m/s speed (with a 0.016 coefficient).

Using the same equation, I go ahead and rerun the number, but adding a distance of 0.1m, a value I used as a good approximation of a reliable accuracy of an Olympic throw, and a time of 0.2s (the approximate time I estimated based on the video), which means a deltaX2 of 0.36m, or 0.596m.

1/2mv2+fapplieddeltaX2 = ffrictiondeltaX Fapplied comes out to 0.326N to 0.526N which is a miniscule amount.

That seems to indicate that a tiny touch DOES have the potential to make a significant difference. Some sources say 0.25 to 0.5N is required for a keyboard press, so its roughly on par with that

But, how much of a difference does the sweeping make on stone speed? Its easy to say that tiny change can impact things, but how does it compare to, say, sweeping hard vs not sweeping?

This study shows a sweeping change of 45+/-8mm. Thus a change of 25% on top of that is not insignificant.

So the last question is, does it make sense for someone to train specifically by cheating this way rather than doing it right and just pushing off with a more accurate force? That's likely going to be subjective, but seems difficult to me.

Who knows, maybe this is a crutch and it is making a difference. Sounds like they need to stop doing it any case, whether a way they've trained or not. Or wear a camera showing they don't touch the rock and just hover their finger behind it.