Contrary to what the headlines suggest, the biggest test of President Obama’s move to normalize relations with Cuba will not be whether the two countries agree to set up embassies in their respective capitals, nor whether there is an avalanche of U.S. tourists to Cuba, but whether Cuba will accept U.S. help to expand Internet access on the island.

In his Dec. 17 announcement of talks to set up full diplomatic relations with Cuba, Obama said that one of the centerpieces of his new Cuba policy is to help connect the Cuban people with the rest of the world. To that aim, Washington will lift U.S. rules that have prevented U.S. companies from exporting smartphones, satellite Internet connections, Internet software and other telecommunications equipment to the island, he said.

But judging from what I’m hearing from well-placed visitors to the island, there are good reasons to be skeptical that the Cuban regime will allow any of this to happen.

Right now, Cuba has the lowest Internet penetration rate in Latin America, and one of the lowest in the world. Only 5 percent of Cubans have access to unrestricted Internet, according to the Washington-based Freedom House’s “Freedom on the Net” report.

Cuba, which has claimed that it cannot expand Internet on the island because of the U.S. embargo, says Internet penetration on the island is at 25.7 percent. In reality, the bulk of that consists of a heavily-censored intranet system that mainly allows access to domestic emails, a Cuban government version of Wikipedia and Cuban websites sympathetic to the regime.

Furthermore, there is only one Internet service provider in Cuba: the government. This has allowed the Cuban regime to keep the population in the dark about the outside world, and about what’s going on inside the island.

Rubens Barbosa, a former Brazilian ambassador to Washington and London and current head of international relations of Brazil’s powerful FIESP industrialists’ association, is one of several well-placed people who have returned from Havana in recent days and report that the Cuban government is highly unlikely to allow larger Internet penetration on the island.

Returning from a week-long visit to Havana, during which he met with Cuban officials and foreign diplomats, Barbosa wrote in Brazil’s daily O Estado de Sao Paulo and told me in a later interview that “the first thing that calls the attention of any visitor is the population’s resignation to its limited living conditions.”

“There are shortages of food and almost everything else, of services, of transportation, of housing, with up to three generations of the same families sharing small apartments in precarious buildings,” Barbosa said.”There is a peaceful political submission, contested by a minority without significance in practical terms.”

As for the ongoing U.S.-Cuba talks to normalize relations and expand commercial ties, Barbosa told me that “Cuba will only allow increased foreign investments in those areas in which the Cuban government is interested in, namely tourism, oil, renewable energies, biotechnology and food.”

Investments to expand Internet access on the island are not on the list, Barbosa said. Much like China and Vietnam, Cuba is embarking on “a gradual economic opening within those areas that are of interest to the state, with a rigid political control by the Party and the military.”

My opinion: If Obama really wants to prove that — in addition to looking good in history books — he wants to help bring about basic freedoms in Cuba, as he has repeatedly stated, he should make increased U.S. exports of Internet equipment and services a key part of his normalization talks with Havana.

Neither a U.S. embassy in Havana, nor a million additional U.S. tourists sunbathing in Varadero beach, nor U.S. exports of paint and building materials for the island’s small private sector, will help open up Cuba’s political system.

Millions of foreign tourists — including nearly two million Canadians and Europeans last year — have long been visiting the island, and European countries and Canada have been exporting goods to Cuba for decades, without any major impact in helping connect Cubans to the outside world, or helping the island emerge from its chronic poverty.

In coming rounds of the U.S.-Cuba normalization talks, Washington should focus on the Internet. And if Cuba balks, as many expect, the United States and Latin America should denounce Cuba for what it is: a military dictatorship that has run out of excuses for refusing to allow its people to access the Internet.