I thought I noticed Flavia training in Jazz sneakers the other day. These are good supporting, and have a split sole allowing you to move through your feet and through the floor and depending on the brand there is a slight shock absorption too. I have noticed male pro's dancing in trainers on occasion too which I found a slight shock but suppose its not that big a deal as again, they would have a shock absorbing sole and be supportive of the feet. I think, from a woman's perspective, I prefer to get my heels on as soon as possible as they definitely alter the way you move and if they are what you are going to be wearing for performing then you might as well get used to them ASAP - I usually learn a dance in jazz sneakers then transfer into my Capezios or whatever shoes I will be wearing for the performance with plenty of time to get used to them. However, whilst shoes are important, they are not quite as important as dancing on a sprung floor. Eg, my training is mainly in Ballet and in regular ballet shoes i.e not pointe or demi-pointe shoes you basically have no support, the shoe is more like a glove, and the strength is built up entirely in your feet and ankles. Most contemporary dancers dance in bare feet or just a thong (FOOT thong, get your mind out of the gutter please!) and once I got on to medals my jazz teacher insisted we danced in bare feet for exams and performance, allowing us to develop and demonstrate the strength in our feet, as jazz trainers can distort the impression of what the foot is doing in the view of an adjudicator and I found regular jazz shoes to be slippy. I think it is important for the female celebs especially to dance in their heels asap as dancing in heels does take a bit of getting used to in terms of balance and the weight being more forward etc. The pro females are probably much more used to their heels and I would imagine it would be much easier to teach at the beginning of the week in shoes such as jazz sneakers, as the male celebs are still getting used to the dance, and accidents (in the foxtrot, quickstep etc) are more likely to happen.
On the other topic, I do believe that most of the training takes place in the dance/aerobics studios of gyms. These most likely have a cushioned floor.