Paul, making a pitch for the Republican Party to a crowd of largely young African-American students on Wednesday, used the presidents' success, despite their drug use, as evidence for the need to eliminate mandatory minimum sentences for drug offenses.

He offered what initially seemed like an allegorical story of two young men, "both … made mistakes" and "were said to have used illegal drugs."

Without giving the two men names, he described their racial and economic backgrounds.

"One of them was white and from a privileged background. He had important friends, an important father and an important grandfather. You know, the kind of family who universities name dorms after. This family had more money than you could count. Drugs or no drugs, his family could buy justice if he needed it," he said.

He added: "The other man also used illegal drugs, but he was of mixed race and from a single-parent household, with little money. He didn’t have important friends or a wealthy father."

"Now, you may think I’m about to tell you a story about racism in America, where the rich white kid gets off, and the black kid goes to jail," he said.

And then he revealed the names of the two men: "Barack ObamaBarack ObamaCongress needs to assert the war power against a dangerous president CNN's Don Lemon: Anyone supporting Trump ‘complicit' in racism DOJ warrant of Trump resistance site triggers alarm MORE and George Bush were lucky," he told the crowd, to laughter.

Obama wrote in his autobiography about his drug use, which included heavy marijuana smoking and some cocaine use throughout his high school and college years. And Bush reportedly used cocaine, and at one point hinted at smoking pot.

"The law could have put both of them away for their entire young adulthood. Neither one would have been employable, much less president," Paul said.

Paul introduced a bill last month, along with Sen. Patrick LeahyPatrick LeahyImmigration battlefield widens for Trump, GOP Grassley shouldn't allow Senate Democrats to block judicial nominees Trump’s rhetoric and bluster could lose US an ally in Mexico MORE (D-Vt.), to give judges more discretion over sentencing and eliminate mandatory minimum sentencing laws.

Paul characterized such laws as "heavy-handed and arbitrary" in his speech.

But he later clarified during the question-and-answer session, that while nonviolent drug users shouldn't be imprisoned, even "benign" drugs, like marijuana, can be harmful. 

“I think that if you use [marijuana] too much, you will lose IQ points. I think if you use it too much, you won’t show up for class,” Paul explained. “I think you’ll eat too many Doritos.”

His comments on Obama, Bush and drugs echoed those he made on Fox News Sunday in late March, after he announced the bill, when he said that if the presidents had gone to jail, "It would have ruined their lives."

Paul differs from his father on marijuana; while his father introduced a bill to legalize pot, Paul is opposed to legalization.