I can not find a positive reference for this claim. But what I've found is the text of the famous roman architect Vitruvius who pities  that a certain law in Ephesus, holding architects responsible for their works, does not exist in roman law:
- [...] When an architect [in Ephesus] was entrusted with the execution of a public work, an estimate thereof being lodged in the hands of a magistrate, his property was held, as security, until the work was finished. [...] But when more than one-fourth of the estimate was exceeded, he was required to pay the excess out of his own pocket.
- Would to God that such a law existed among the Roman people, not only in respect of their public, but also of their private buildings, for then the unskilful could not commit their depredations with impunity, and those who were the most skilful in the intricacies of the art would follow the profession. Proprietors would not be led into an extravagant expenditure so as to cause ruin; architects themselves, from the dread of punishment, would be more careful in their calculations, and the proprietor would complete his building for that sum [...]
The book is dated around 15 BC  - certainly not quite the end of the roman empire; so if such a law or customs existed, one should probably look after this date or investigate in military codices.
Another great source for the history of bridge building is "Berühmte Brückenbauer: Ihre Zeiten und Bauwerke" . It's full of trivia and references and deals a lot about ancient roman engineering - but this certain kind of punishment or however you might call the claim, is not mentioned.
- Marcus Vitruvius Pollio. "De Architectura", Liber X, Introduction, paragraphs 1-2. Translation by Bill Thayer. Undated. URL: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/10*.html . Accessed 2013-12-17. (yes, there's really an asterisk in the URL)
- Ditchen, Henryk; Glomb, Jozef. "Berühmte Brückenbauer: Ihre Zeiten und Bauwerke". Logos Verlag Berlin GmbH. 2012. URL: http://books.google.de/books?id=U5iUF7twBBgC . Accessed 2013-12-17.