I think structurae has arrived at their "57 m" by dividing the total length by the number of pillars (1135/20 = 56,7). However, they did not calculate the width of the pillars, as a bridge span is in my understanding defined as the free space between two pillars, so you are correct that they number is strange. Anyway, the bridge's wooden arches are clearly segmental, so assuming a record span is not unrealistic: www.hdg.de/eurovisionen/html/br2_1.html 

 As for Alconetar, go to Google Images. You can see that the three surviving arches are segmental arches, but
 these look a bit like much later amendments
 these segmental arches had very conventional span/rise ratio, so the advantages of the seg. arch bridge were not fully exploited

 The arches of the Pons Fabricius look rather semi-circular to me.

Could you uncover your references? As for Roman bridges there is the classical: Colin O'Connor, Roman Bridges, Cambridge Univ. Press (1994) ISBN 0-521-39326-4