On a trip to Havana in the late 1990s, I toured the restoration of a 17th century convent with a Cuban architect. He told me the project was having trouble getting replacement floor tiles because of the U.S. embargo. I smiled and told him there was no blockade of the island and that the tiles could be sourced in Mexico. He grinned back at me.

“Well, OK,” he said. “The real problem is that we don’t have any money to buy them.”

Cubans are programmed from an early age to complain to anyone who will listen that “el bloqueo” is the cause of the island’s dire poverty. They know it’s a lie. But obediently repeating it is a survival skill. It raises the odds that the demented dictator won’t suspect you of having counterrevolutionary thoughts, boot you from your job, kick your children out of school and haul you off to jail.

President Obama appeared to be trying to prove his own revolutionary bona fides when he announced on Wednesday new diplomatic relations with the military dictatorship and plans to make it easier for Americans to travel to the island and engage in commerce with Cubans. He repeatedly linked the isolation of the Cuban people to U.S. policy, as the regime teaches Cuban children to do. He complained that the embargo strives to keep “Cuba closed off from an interconnected world.” In a reference to the limited access that Cubans have to telecommunications, he said “our sanctions on Cuba have denied Cubans access to technology that has empowered individuals around the globe.”

Even the humblest Cuban peasant would split his sides laughing if he heard those statements, which none did because they do not have access to anything other than Cuban state television—speaking of isolation. Cubans know that the island is not isolated from foreigners. According to Cuban statistics in 2013 there were 2.85 million visitors to the island of 11 million inhabitants. These included European, Chinese, Latin American, Canadian and American tourists and investors. In the first six months of this year, according to The Havana Consulting Group, there were 327,000 visitors to Cuba from the U.S.

The isolation (news flash Rand Paul ) is caused by the police state, which controls and surveils foreigners’ movements, herding most visitors into resort enclaves. Foreign journalists who vocally oppose the Communist Party line are not allowed into the country.

More visitors won’t do anything to reduce Cuban poverty. The regime pockets the hard currency that they leave behind and pays workers in worthless pesos. Foreigners who decide to reward good workers without state approval can face prison.

It’s true that the Cuban people lack access to technology, but Mr. Obama’s suggestion that it is because of the embargo is a howler. Carlos Slim , the Mexican telecom monopolist and global player; Telefónica , the Spanish broadband and telecommunications provider; Vietnam’s Natcom; Ireland’s Digicel and countless other companies can do business on the island. But they can’t provide Internet access in homes because the state prohibits it.

U.S. telecom companies are lobbying Washington to be able to do business with the dictator. So to peddle the idea to the rest of us, Mr. Obama claims that this small, backward Caribbean country is a huge untapped export market. Question: How come the likes of Mexico and Spain haven’t flooded the virgin paradise for capitalists and turbocharged the Cuban middle class? Maybe because a couple of hoodlums have rigged the game. They decide who and what enters the country, treat Cubans like slaves, and arbitrarily jail foreign entrepreneurs and take property when it suits them.

Some delusional pro-market pundits think the anti-market Mr. Obama is suddenly pushing their ideas in Cuba. Mr. Obama wants us to believe that when Americans do business in Cuba, Cubans will be empowered. Funny that he didn’t feel that way about helping democratic Colombia when its U.S. free-trade agreement was up for ratification. Back then the White House was fretting about Colombian workers’ rights. Now, well, never mind.

The Castros are in full-blown panic mode because Venezuela, which has been their financial lifeline for 15 years, is broke. The last time things were this bad, when Soviet subsidies dried up in the early 1990s and the regime ran out of money, Castro introduced the “special period.”

Cubans were permitted to run restaurants in their homes, operate taxis and provide other services to foreigners and locals. As entrepreneurship blossomed, the state began to lose the absolute control it had relied on since 1959. Fidel clamped down as soon as Cuba stabilized.

Now the gangsters are again on the ropes. If they can up the number of U.S. travelers to the island and later wrangle multilateral funding now blocked by the U.S., they might squeeze by. But if not, the dictatorship is likely to come unglued, which raises the question of just who Mr. Obama is trying to help by stepping in now.

Write to O’Grady@wsj.com