Your second paragraph (sort of) contradicts the first: it says that (some) groupon users will never return unless presented with another groupon. No repeat/loyal customers.
That might be the problem with groupon: the people most likely to use groupons are the ones least likely to become loyal customers and the least likely to effectively recommend your business to their friends because all their friends know they only went there due to the groupon.
Even if they don't come back, it's still better to have the Groupon chasers in your studio. You get paid at least a little bit if they buy a Groupon, compared to nothing if they don't. The marginal cost to a Yoga studio of adding another student is zero.
Of course this doesn't apply if you're running close enough to capacity that the addition of more students will degrade the experience for everyone else, but a lot of yoga studios don't have that problem, especially not at off-peak hours.
Right, it's a double-edged sword. 'Premium' customers find coupons unseemly and wonder why a good business needs to offer coupons (I have this knee-jerk reaction myself, as I didn't grow up in the US perhaps). On the other hand, groupon offers a level of exposure that may be compelling. I think that the yoga studio owner has come to the right conclusion to her - grow her business organically based on quality.
That might be the problem with groupon: the people most likely to use groupons are the ones least likely to become loyal customers and the least likely to effectively recommend your business to their friends because all their friends know they only went there due to the groupon.