This scene is based on an episode in the life of Meyer Lansky, a big-time gambling gangster on whom the Roth character is very closely based:

The US Justice Dept. was harassing Lansky, so he tried to ease the pressure on him by moving to Israel to take advantage of Israel's "Law of Return," which allows any Jew (defined as someone who was born to a Jewish mother) to live in Israel and become a citizen. Israel's Supreme Court turned down his application. Lansky sought to flee to various South American countries, but the FBI was on his case every time. After nearly 48 hours in South American airport immigration offices, he returned to Miami. There he faced four felony charges (one local to Miami/Dade, three Federal). He managed to beat all four charges, lived to age 80 and died peacefully in bed.

Of course, Lansky wasn't facing a foe like Michael Corleone, as was the Roth character in the movie. The bit of dialog that Roth had with the reporters at the Miami airport didn't make it clear if he'd been trying to flee Michael, or "the goddamn Justice Department," as he said at his birthday party in Havana.