Update: It seems to me that Samsung did clarify this issue saying that this is not a glass-based display, but I'm not 100% sure yet.
On October 9th, Samsung launched the world's first device with a flexible OLED display, the Galaxy Round smartphone - with it's curved 5.7" Full-HD flexible Super AMOLED. Strangely Samsung does not refer to this display as a YOUM display, which is the brand name for plastic-based OLEDs they launched at CES 2013.
In their PR, Samsung also never mentioned that this display is "unbreakable" - which is one of the biggest advantages of plastic-based OLEDs. Samsung's design is also much less exciting that the design prototypes they unveiled at CES that used a YOUM display. A couple of weeks ago I thought that perhaps this display uses a glass substrate and not a plastic one, which will explain everything. I checked with my sources and they said that it is using plastic and this is a YOUM display.
But now I read in TouchDisplayResearch's blog that their analysts also speculate that this display uses a glass substrate. So now I'm not sure and personally I think Samsung wouldn't have missed the opportunity to announce an obvious achievement such as an unbreakable, durable display. So I now estimate that this display actually does not use a plastic substrate. It's true that Samsung managed to achieve a curved display in a phone, but perhaps this is not quite the technology breakthrough we assumed.