If Bush had conceded to Gore in 2000, Gore would have become president, not Dick Cheney. So whoever responded by saying what you quoted didn’t know what they were talking about.
Are you telling me that if Donald Trump conceded the election to Hillary Clinton after he had won 300+ electoral votes, then she would have become President? I don't think so.
Section 3 of the 20th Amendment would almost certainly dictate the scenario in this case.
“Concessions” are not legally binding in any way.