In fact, the PRI had already begun changing in the 1980s. Stung by public outrage over some of the economic messes it had made, the party oversaw the privatization of inefficient state-owned industries that were once vast reservoirs of patronage jobs. It gradually allowed electoral reforms that finally gave opponents a chance to win elections.
During its time in power, the conservative National Action Party tried to lend a more informal air to the presidency. The office also became weaker in the face of the rising independence of the Supreme Court as well as state governors, many from opposition parties who owed no allegiance to the president. Opposition also increased in Congress.
Ruben Aguilar, who was a spokesman for then President Vicente Fox, the National Action candidate who defeated the PRI in 2000, said he's willing to give the PRI "the benefit of the doubt," in part because the party is known for pragmatism. It never had much ideology beyond keeping itself in power, and returning to old abuses could be suicidal.
"If they tried to return to the old ways, it would be very clumsy, very shortsighted," Aguilar said.
Some things are clearly gone forever, such as the PRI's role as "daddy government," handing out state-built housing and jobs at state-owned enterprises. The government firms have been privatized and the oil-fattened government budgets have shrunk.
Instead, Pena Nieto aims to fulfill his main promise, to create more jobs and boost economic growth, by going even further in developing the private sector. He also pledges to preserve the main achievement of the two National Action Party presidents: responsible government finances and macro-economic stability.
The PRI was never a classic, bloodthirsty dictatorship. It often bought off enemies and pardoned when it could.
When students at the national university pelted President Luis Echeverria with rocks in 1975, blaming him for ordering the shooting of student protesters seven years before, Echeverria simply left the campus.
While Echeverria imprisoned leftist rebels or allowed them to vanish in the maw of the security system, his successor pardoned those who remained jailed, giving rise to a generation of opposition politicians.
Many Mexicans retain a cynical fondness for the old party's populism, as reflected in one old saying that translates roughly: "They stole, but at least they let others get what they dropped."
Some expect a comeback of the PRI political style that combined a devotion to high-flown rhetoric, strict obedience among party members and an unquestioned respect for the authority of the president.
"I think we're going to see a lot of the old informal rules come back," said Andrew Selee, director of the Washington-based Mexico Institute.
He noted PRI members show tight party discipline and try to keep political disputes behind closed doors. That could reinforce the PRI's claim that it knows how to govern efficiently, unlike the two National Action presidents, who at times seemed to flounder.
The PRI's discipline is enshrined in another old saying. Counseling against jostling for political position, late PRI union boss Fidel Velazquez counseled, "He who moves around doesn't show up in the photo."