Wright S. answered 03/15/19
MIT Political Science PhD candidate; history, politics, literature
Your supposition is correct. When the Bay of Pigs invasion was carried out, President Kennedy was concerned about the appearance of American involvement, and while the military asked for the use of advanced American aircraft to support the invasion, Kennedy refused to try to limit the public links between the invasion and the United States. American planners also believed that the Castro regime was weaker than it in fact was, leading them to think that a smaller invasion force would find supporters amongst the populace who would then rise up to overthrow Castro.