I thought this was a fascinating observation so I'll try and recast it into the UK situation.
Imagine a mid level supermarket, say, a Waitrose. Imagine then that a cheapy cheapy place opens next door, say an Iceland or a Lidl.
Imagining? Good, now, what happens to the prices in the Waitrose? Do they rise or fall?
Ah, yes, we've our old correct answer in economics again, "it depends".
If that Waitrose faced no competition, or very little competition, then pries would fall as the introduction of competition would mean they have to cut margins in order to retain much of their custom.
However, if the market was in general competitive to start with, then the Waitrose (please note, these names are indicative, just to set the scene, not descriptions of actual stores) would have already pared margins to retain custom. It would be doing its best to appeal to both the high income groups and the price motivated shoppers. Then in comes the determinedly low cost store: they're going to suck away those price conscious people almost whatever the Waitrose does. There just isn't much point in trying to cut pries to meet them. In which case the Waitrose prices might actually rise: better to make higher margins off the high income groups (who wouldn't be seen dead in an Iceland after all, they use that common girl in their ads) and accept the loss of the price driven shoppers.
I think that's a very nice little demonstration of that most important answer in economics. What happens when something changes really does depend, depends upon reactions to it, what the initial set up was and so on.
Do note though that despite the Waitrose prices rising, shoppers themselves are better off. Those who willingly pay the higher prices are clearly willing to do so in order to not have to shop with Ms. Katona, those willing to chase prices are clearly made better off by being able to do so. And we are, after all, trying to get this whole game operating in favour of the consumers.