This behavior has been well documented in Japanese crows, but Cristol et al (the contradicting paper in the question) did not observe it in American crows.
This Ph.D. dissertation discusses the findings of Cristol, as well as another paper by Nihei which documented the behavior in Japanese crows.
While [Cristol et al.] are careful to note that they cannot conclude definitively that crows never use cars intentionally to crack open nuts, their unfortunate title choice (“Crows Do Not Use Automobiles as Nutcrackers”) does not appropriately reflect their findings. This is especially problematic as this behaviour had already been well-documented in crows in Japan in 1995 (Nihei, 1995), two years before Cristol, Switzer, Johnson, & Walke published their article (1997). This example demonstrates the importance of recognizing that animals from different geographical locations can develop different problem solving abilities, even if they are members of the same species.
Later in the same dissertation,
These [Japanese] crows have been well documented to use vehicles to crack open nuts that they could otherwise not open. The crows carefully place the nuts on busy streets and wait for vehicles to come by and run over the nut, and therefore crack it open so that the crow can eat the meaty inside of the nut. Not only do the crows choose their roads carefully, they also carefully choose the locations on the road where they leave the nuts. Busy traffic is good for cracking open nuts (the more vehicles that pass by, the sooner the nut will likely be run over), but busy traffic also makes retrieving the cracked nuts more difficult. In order to make retrieving cracked nuts easier, the crows will place their nuts on roads in locations that are near pedestrian crossings and wait for the traffic to stop before going on to the road to retrieve the cracked nuts (Nihei & Higuchi, 2002; BBC Wildlife, 2007). In this example, the crows are clearly using the vehicles as nutcrackers, despite not actually having any control over the vehicles.
Note: I cannot find an English version of (Nihei, 1995), but here is the Japanese version. Google translate roughly confirms the Ph.D. dissertation's summary.
A different short scientific article disputes the conclusions of Cristol et al for American crows specifically, but provides only anecdotal observations.
Cristol et al. (1997) disputed the intentionality of the latter behavior, but on at least eight occasions I observed Western American Crows (C. brachyrhynchos hesperis) in Encino, California, land on wires above a road, drop pecans onto the pavement, and not fly down to inspect or retrieve them until a car had passed.
As discussed in this scientific article, American crows regularly drop nuts onto hard surfaces to break them. Young crows learn this behavior from older crows, which can take up to a year. This suggests that the behavior could have spread through Japanese crows, but not American crows.