Putin said he was not aware of the comment, Albright denies ever making it, and no one else seems able to provide any evidence that she did.
But this hasn't stopped Putin and others from attributing these thoughts to foreign figures who they say wish Russia harm.
Sibert, 70, a mechanic who works at the Institute of Nuclear Physics in Novosibirsk, brought up the purported statement in a question during Putin's annual call-in show last month.
"I know some politicians entertain such ideas in their heads," Putin replied, adding that Russia was able to and would protect its natural resources.
The only problem is that Albright, who is now a principal at the Albright Group strategic management and lobbying firm, denied through a spokeswoman that she ever entertained the idea.
"I did not make that statement, nor did I ever think it," she said.
On Tuesday, Sibert was unable to provide a source for the alleged quote, or even a guarantee that he had heard it.
"I don't know. I might have made a mistake," he said by phone from Novosibirsk. "But I don't think I did."
Sibert said he was not instructed in any way to ask his question on the call-in show but that the event's organizers were aware of its content.
And he remains convinced that the idea he raised was an accurate one. "The question I asked is just the tip of the iceberg," he said.
More of that iceberg was visible Sunday, during celebrations for People's Unity Day.
At an event on Red Square, Robert Shlegel, an activist with the pro-Kremlin Nashi youth group, raised the issue again. Putin, in a veiled reference to the United States, described some world leaders as having "just lost it" because of Russia's wealth in natural resources.
Shlegel said Tuesday that he didn't know whom Putin meant but that opposition movements like The Other Russia were playing into the hands of the country's enemies because they were weakening the country.
As for the elusive statement, he said Albright had made it during an interview with Alexei Pushkov on the "Postscriptum" news analysis program in 2005.
"The president's words could hardly have been unfounded," Shlegel said.
But Oksana Yanovskaya, editor in chief of "Postscriptum," said Tuesday that Albright was never interviewed on the program and that Pushkov had just cited a statement that he had seen or read somewhere else.
"I am absolutely sure there was no interview," she said, although she added that Pushkov had met Albright at some event. Yanovskaya said she had called Pushkov, who was out of the country, on Tuesday and that he couldn't remember where he had seen the quote.
"Many people were citing it back then," Yanovskaya said.
In perhaps the strangest part of the story, there are those who argue that it doesn't matter what Albright said -- they know what she was thinking.
Boris Ratnikov, a retired major general who worked for the Federal Guard Service, said in a December 2006 interview with government newspaper Rossiiskaya Gazeta that his colleagues, who worked for the service's secret mind-reading division, read Albright's subconscious a few weeks before the beginning of the NATO bombardment of Yugoslavia in 1999.
Albright, who as secretary of state played a major role in the lead up to the attacks, was one of the main targets of Russian criticism of the bombing campaign.
Apart from her "pathological hatred of Slavs," Ratnikov said "she was indignant that Russia held the world's largest reserves of natural resources."
On Tuesday, Ratnikov, 62, said he hadn't been part of the mind-reading experiment but had worked as an analyst on the data produced by his colleagues in the study. He said the mind-reading process involved using a picture or some other image of the person under study.
"By tuning in on her image, our specialists were able to glean these things," he said.
Others say you don't have to be a mind reader to understand that some outsiders would like to lay their hands on Russia's wealth.
Kremlin spokesman Dmitry Peskov said Tuesday that he was not sure which outside forces Putin was referring to on Sunday or whether the Albright quote was authentic.
He did say, however, that it was "obvious that Russia had ill-wishers" that don't like the revival in the country's assertiveness and are irritated by its newfound economic power and global weight.
Alexei Sidorenko, coordinator for the society and regions program at the Carnegie Moscow Center, said that although the alleged quote had been making the rounds in Russian on the Internet since 2005, his center had been unable to find any mention of it in the English-language media.
He said conjuring the image of an external enemy to mobilize the population and deflect attention from domestic issues was nothing new in politics, and the fact that Albright was no longer in government meant she had no official channels through which to respond.
"The Kremlin's entire political strategy at present rests on consciously created myths, and they are beginning to dominate the agenda," Sidorenko said.
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