Did an ancient Roman invent "flexible glass" ?

From an interesting post this week at Beachcombing's Bizarre History Blog:

The story appears first in Petronius’ Satyricon (51 – early first century AD): ‘However, there was an artificer once who made a glass goblet that would not break. So he was admitted to the Emperor’s presence to offer him his invention; then, on receiving the cup back from the Emperor’s hands, he dashed it down on the floor. Who so startled as the Emperor? But the man quietly picked up the goblet again, which was dinted as a vessel of bronze might be. Then taking a little hammer from his pocket, he easily and neatly knocked the goblet into shape again. This done, the fellow thought he was as good as in heaven already, especially when Emperor said to him, ‘Does anybody else besides yourself understand the manufacture of this glass?’ But, on his replying in the negative, Emperor ordered him to be beheaded, because if once the secret became known, we should think no more of gold than of so much dirt.’

Beachcombing notes that the story was retold two centuries later, and a different incident was reported in 79 AD:

Pliny the Elder (obit 79 AD), a near contemporary, reports that in the time of Tiberius, forty years before he brought out his Natural History, a new kind of flexible glass was produced that the Emperor did everything possible to outlaw, even destroying the workshop of the inventor (‘totam officinam artificis eius abolitam’).

Fable/myth?  Or true?  There's a discussion at the link, with a addendum suggesting that the Romans might have invented tempered glass.  A different possibility that occurred to me is that a craftsman could have acquired a large lump of relatively clear amber (does amber come in clear form?) and worked into the shape of a glass (? is that possible).

If you have any ideas, please insert them in the comments here, or at the original link.