Strangely perhaps, in the past the PRI never actually ruled Mexico. It ran a skilled vote-gathering (or vote-fixing) operation, but the country was run by a political bureaucracy in league with other power centers, such as banks, labor unions, the army, television magnates and industrial moguls. The PRI provided a rubber-stamp Congress and, every six years, the outgoing president picked his successor.The most obvious error is that it's not an either-or proposition--i.e. either the banks, et al or the PRI ruled Mexico. Of course, they all did, as is the case in most countries, where any number of power centers play a role in making the system hum.
But beyond that, the PRI may not have run the country, depending on how you define the word, but it indisputably was the primary mechanism around which the country organized itself. The party co-opted all of the above into a system over which the president, a priísta, reigned supreme. The other power centers could throw their substantial weight around and even push back against other purely political actors, but they did so within the confines of the system that the PRI held up. Perhaps the party didn't run Mexico the way that Jobs ran Apple, but getting such a wide range of actors to buy into a common system over which their leader held the most sway seems a pretty close approximation for running a nation. Any other explanation seems like semantic hair-splitting.