The story is also told by Cassius Dio (57.21.7), who uniquely knits it together with another tale, where the unfortunate artisan excites the admiration and then the jealousy of Tiberius by devising an ingenious way of repairing a portico. The story is also retold by Petronius' Satyricon (51), but there the name of Tiberius is omitted altogether - the artisan approaches an unnamed Caesar with his invention. The Chronica Maiora of Matthew Paris places the story in the year 21, but whether this otherwise unattested date has any significance at all is doubtful.
As Pliny (36.195) says, however, this story is repeated with more frequency than truth, and indeed the whole tale of the unfortunate artisan approaching the emperor, whether Tiberius or an unnamed Caesar, seems to have been an apocryphal fable of no factual value. Several modern writers have come up with ingenious explanations, desperately attempting to justify the ancient fable, but none successfully. The most extensive, philological investigation on this story was made by Lassen 1995 (https://scholarworks.iu.edu/journals/index.php/cl/article/view/34890), concluding that the story told by Pliny, Dio and Petronius is an iteration, indeed the first known iteration of a folk-motif: the 'Impossible Product'. Lassen noticed that the period when this story first circulated, i.e. the first century, saw a quick escalation of glass-making in the Roman world, and points out that:
'The historical period in which we find the first examples of this legend was, we may safely conclude, a time of relatively fast changes in the technology; subsequently, one must also surmise massive changes in the marketing of glass. About the time of the reign of Tiberius, the status of glassware thus changed from being a luxury, exclusively for the rich, to a product which could be produced at a sufficiently low cost to appeal to the ordinary customer. Whereas Petronius, and Pliny's accounts appear to display exactly the kind of open-ended attitude to the possibility of further improvement of the novel product that one would expect in such a context, Dio's version reflects a much more unimaginative attitude to glass, most likely a result of well over a hundred years of acquaintance with this material.' (Lassen 1995, p. 6)