As President Trump faced a barrage of criticism last summer over the former Wall Street executives and other ultra-wealthy people serving in his administration, he offered a characteristic rationale: The appointees, he suggested, were too rich to have financial conflicts of interest.

“They’re representing the country,” Mr. Trump said in June at a rally in Iowa. “They don’t want the money.”

But a cascade of revelations surrounding his advisers’ business holdings — including news this week that the commerce secretary, Wilbur L. Ross Jr., retained business ties to a Russian oligarch subject to sanctions — has thrust into view an inescapable contradiction between the financial transparency expected in public service and the realities of the modern global rich.

Mr. Trump has assembled the wealthiest cabinet in American history, and also a deeply conflicted one, despite federal rules requiring appointees to relinquish or distance themselves from assets that would conflict with their government responsibilities. Even now, the Trump team has holdings that are spread across myriad industries and hidden from the public behind layers of trusts and shell companies. Some of that secrecy has been washed away in recent months by press reports and by the leak of millions of documents from Appleby, one of the world’s leading offshore law firms.