Not any more. In the most surprising fall-out so far from last week's assassination of the presidential candidate Luis Donaldo Colosio, Mr Cordoba, 43, was yesterday removed as Chief of the Presidential Office. His sudden appointment as Mexico's envoy to the Washington-based Inter-American Development Bank, a newly created post, was seen as anything from a kick downstairs to an enforced exile.
The fact that it was announced not by Mr Salinas but by the Finance Minister, Pedro Aspe, was seen as something of an affront to Mr Cordoba, widely resented because of his foreign roots and the fact that few, if anyone, could talk to Mr Salinas without going through him.
Worse, to some Mexicans, Mr Cordoba's job-switch carried with it more than a hint of stigma amid widespread suspicion that Colosio's murder in Tijuana was part of a conspiracy from within the ruling Institutional Revolutionary Party (PRI). Colosio was the party's candidate to take over from Mr Salinas in presidential elections on 21 August.
Like God, who has been in power even longer, the PRI works in mysterious ways. A day before Mr Cordoba's removal from the cradle of power, the party had chosen as its replacement candidate Ernesto Zedillo Ponce de Leon, 42, who had been Colosio's campaign manager but was also known as Mr Cordoba's protege. Whatever the significance of his own job move, Mr Cordoba has undoubtedly seen 'his man' appointed candidate and favourite to govern Mexico until the year 2000.
The party that has ruled Mexico uninterrupted for 65 years has been badly split into at least three factions. Hence, the speculation that elements within the PRI itself may have behind Colosio's assassination. The man accused of shooting Colosio, Mario Aburto Martinez, 23, told interrogators: 'I will not talk even if I am tortured.' A former Tijuana policeman and PRI member helping guard Colosio, Tranquilino Sanchez, has been detained for allegedly helping the gunman; another former policeman was found to have gunpowder traces on his hand; yet another former policeman, questioned but since released, was said to have been 'hanging around' with the gunman for weeks before the shooting.
As a French citizen, Mr Cordoba was a campaign adviser to Francois Mitterrand before coming to Mexico in 1978. He was aligned with Mr Salinas when the latter was budget and planning minister under the previous president, Miguel de la Madrid. When Mr Salinas became President in 1988, Mr Cordoba, who became a Mexican citizen in 1985 but whose foreign parentage eliminated him from any presidential aspirations, became the Chief of the Presidential Office.
Naming Mr Zedillo as party candidate then getting rid of Mr Cordoba does not seem to add up. Some analysts believed a trade-off had been agreed whereby Mr Cordoba, widely unpopular and likely to have been out of work at the end of Mr Salinas's term, had agreed to the bank job for two reasons. First, it would remove his burden of unpopularity from Mr Zedillo's shoulders should the latter win the presidency. And second, being Washington-based, he could become an important link between Mr Zedillo and the White House.
The PRI now faces its toughest year, with a grey, inexperienced second-choice candidate seeking to postpone what now seems the party's inevitable fall from power, sooner or later. Despite his generally positive image abroad, Mr Salinas has entered the 'lame duck' period, when outgoing presidents traditionally stand back and leave the candidate to take the limelight.
'The PRI is a dinosaur that deserves extinction,' said Enrique Krauze, a Mexican historian and political analyst, in an interview this week. 'It's hour came and it should have changed. The PRI has had every imaginable defect. It has been corrupt, it has treated campesinos (peasants) like political cattle and, at local and state level, there has been a significant level of violence.'
An opinion poll this week suggested that revulsion at Colosio's murder had boosted the PRI's potential share of the presidential vote from less than 50 per cent to 65 per cent. It was carried out before Mr Zedillo's nomination.
The influential pro-government television channel, Televisa, has been running videoclips of Colosio regularly, suggesting it intends to continue pushing the widely liked politician as a martyr and ghost candidate.