One of the great things about ORBIS is that they exhaustively cite their sources, which can be found here. The number that they generate is based on numerous archaeological studies, and they cite those sources to back it up. Here's what they have to say in the "Building" section:

Roman roads were used by a wide variety of pedestrians, animals and vehicles, and at an even wider variety of velocities. Time costs were determined not only by means of transport but by road quality, the spacing of suitable rest stops, grade, obstructions such as bodies of water, and seasonal constraints from spring floods to summer heat and winter ice and snow. The model captures only the most important types of time cost in what is inevitably a highly generalized fashion. Numerous studies were employed in establishing simulation parameters (key works include Ludwig 1897; Ramsay 1904; Riepl 1913; Renouard 1962; Vigneron 1968: 134-7, 171-6; Chevallier 1976: 191-8; Dubois 1986; Cotterell et al. 1990: 193-233; Laurence 1999: 78-94; Kolb 2000: 308-32; Matthews 2000; McCormick 2001: 474-81; further on antiquity, see also Hunter 1913; Ramsay 1925; Yeo 1946; Eliot 1955; Forbes 1955: 131-92; Burford 1960; Engels 1978: 15-6; Röring 1983; Sippel 1987; Hyland 1990; Polfer 1991; Stoffel 1994: 161-5; Erdkamp 1998: 72-3; Roth 1999: 205-13; Raepsaet 2002, 2008; Adams 2007; and for further comparanda, e.g., Leonard 1894; Renouard 1961: 110-17; Goitein 1967: 290; Clark and Haswell 1970: 202; Leighton 1972: 48-124; Brühl 1986: 66, 163; Ohler 1989: 97-101; Castelnuovo 1996; Silverstein 2007: 191-3). The considerable amount of relevant scholarship – much more substantial than for sea and river transport costs – makes it impossible to provide even a short review of the complexities of the material (for which see Scheidel in preparation).

Mean daily travel distances have been set at 12 kilometers per day for ox carts, 20km/day for porters or heavily loaded mules, 30km/day for foot travelers including armies on the march, pack animals with moderate loads, mule carts, and camel caravans,[18] 36km/day for routine private vehicular travel with convenient rest stops, 50km/day for accelerated private vehicular travel, 56km/day for routine travel on horseback, 60km/day for rapid short-term military marches without baggage, 67km/day for fast carriages (state post or private couriers), and 250km/day for continuous horse relays (Scheidel in preparation). Except for the final option, which is primarily meant to provide an absolute speed ceiling for multi-day terrestrial information transfer, these transport options are predicated on movement during daytime. Adjustment for night travel would produce higher rates but would usually be feasible only in the short term.

The model seeks to generate values that would, on average, have been sustainable for days or weeks. Just as in the case of sea and river routes, the objective is to approximate the statistically average experience of a large number of travelers, an approach that necessitates critical engagement with individually reported performance times (Scheidel in preparation). In the absence of experimental data, the question of how the generally high quality of Roman surfaces affected travel speed compared to the experience of later periods of premodern history is difficult to address. Roman carriage design (e.g., Röring 1983) and harnessing systems (e.g., Raepsaet 2002, 2008), both of which continue to be subject to debate, were vital determinants of actual performance that complicate any attempt at comparison. To name just one example, comparative data suggest that even though by the late eighteenth century, improvements in roads and equipment sometimes enabled French fast carriages to cover considerably larger daily distances than in previous centuries, even then speeds that exceed corresponding values applied to our model simulations were confined to a few privileged routes (e.g., Renouard 1961: 116; Vigneron 1968: 171-2). We cannot therefore presuppose Roman travel speeds that were consistently far superior to those encountered in other premodern communication systems. Most Roman evidence is consistent with this conservative approach (e.g., Kolb 2000: 321-32 and Scheidel in preparation contra Laurence 1999: 81-2).

So, it's reasonable to trust the scholarship they did, but I'd also love to hear from someone with a current JSTOR subscription to see what specific evidence comes from the cited sources.