The United States have dominated the biennial event since its inception, winning nine and tying one of the last 10 meetings since 2000.
In fact the International team's only victory came in 1998 and their chances in the 14th edition have not been helped by the absence of Open champion Cam Smith, Marc Leishman, Abraham Ancer, Charl Schwartzel, Branden Grace, Louis Oosthuizen, Carlos Ortiz and Joaquin Niemann, who have all signed up for the Saudi-backed breakaway.
As the Presidents Cup is sanctioned by the PGA Tour, who banned all the rebels, Immelman has found himself hamstrung when it comes to selection.
"What stopped me (picking those players) is the fact that when I was made captain we signed up to a specific set of rules," he told a press conference at Quail Hollow in Charlotte, North Carolina.
"This event is owned and sanctioned by the PGA Tour and our team is a team that plays by the rules. We're a team of our word. We're a team of honour.
"Every single player I spoke to from early on in this process knew exactly what the situation and the consequences were going to be and they knew that if they made certain decisions, it was going to be highly unlikely they were going to be able to represent the International team, so that went into their decision-making.
"All the cards were out on the table, and everybody knew where they stood."
While the United States also have a number of golfers missing - the likes of Dustin Johnson, Bryson DeChambeau, Patrick Reed and Brooks Koepka - captain Davis Love III can still call upon five of the world's top 10 and 11 of the top 20.
The best the International team can boast are the 16th, 19th and 20th top-ranked players and that makes the hosts overwhelming favourites.
"Am I worried about losing the Presidents Cup? I'm only worried about sitting guys out right now," said Love.
"We're used to being called the favourite - even when we lose three Ryder Cups in a row, they tell us 'Oh, but they're the favourite'.
"The other captain or the other team or you guys remind us that we're the favourite so we're used to that."