DUBAI, United Arab Emirates — Marooned outside South Africa, Ajay Gupta has been obsessively following the news from home with increasing frustration. Nearly every day for the past couple of months, witnesses at a high-profile inquiry on corruption have painted his family as the masterminds of the government looting that has engulfed the nation.

The accusations infuriate him. But Mr. Gupta and his two brothers, who left South Africa early this year when President Jacob Zuma was forced out of power, have no plans to go back and give their side of the story — at least not yet. They say they fear wrongful arrests if they return to South Africa, a country where their power appeared uncontested less than a year ago.

The inquiry’s leaders have rejected the Guptas’ offers to testify by video conference or other means — creating the possibility that a wide-ranging government inquiry determined to ferret out the truth will not hear from some of the main characters.

“I’m not saying that I’m not coming to the commission,” Mr. Gupta, the oldest brother, said in Dubai, where the family is now based. “I will, but not this moment.”