No, I said it correctly.

From: https://www.ucpress.edu/books/the-united-states-of-war/paper (I'm sure you can search it up, if you CBA):

"In geopolitical terms," writes historian Alfred McCoy, the United States "became history's most powerful empire because it was the first, after a millennium of incessant struggle, to control 'both ends of Eurasia,' " with bases from the British Isles through Southeast Asia to Japan. To guard the empire, the U.S. military had 2.6 million active duty troops; 2,650 ships and 7,195 Navy combat aircraft; 15,000 Air Force fighters, bombers, and transport aircraft; and nuclear weapons ready for launch from the air, the land, and the sea.9 The growing nuclear weapons arsenal of the Soviet Union played some role in the base proliferation: more U.S. bases meant more targets and dispersed forces. The growing fear of a nuclear-armed Soviet Union likewise played an important role in governments agreeing to a U.S. presence. "Viewed from one perspective, this was an act of [U.S.] benevolence," writes foreign bases expert Amy Holmes. The United States was providing protection. On the other hand, other nations were ceding a significant degree of sovereignty to the United States (while also turning themselves into targets for Soviet missiles).10

In Portugal "the supersensitive question of Portuguese sovereignty was constantly being raised before our negotiators," reported Col. Lawrence C. Coddington, Air Force Deputy Assistant for Air Bases. "Every point of issue revolved around the question of sovereignty and were [sic] resolved only after lengthy discussions on many proposed drafts." Coddington acknowledged that "the agreement as written does not meet the ultimate in Air Force desires." But, he continued, "it must be kept in mind that the Air Force cannot hope to achieve its desired ultimate in operating rights in small foreign countries purely because of that country's jealousy over its sovereignty."11

The sensitivity of the Portuguese government about its loss of sovereignty was common among countries hosting U.S. bases. The rapid requests for the Yankees to leave after World War II revealed this. Even with growing fears of a clash between East and West, base negotiations were often difficult. Generally, they revolved around the degree to which U.S. forces would enjoy "extraterritoriality"—that is, the extent to which U.S. forces would be free from local laws, free from local prosecution for committing any crimes, and free to conduct military operations without restraint or consultation with the host nation. In other words, negotiations focused on how much effective sovereignty the U.S. military would have on foreign soil and thus how much sovereignty a host country would give up. Even with the United States' closest allies, such as Great Britain, sovereignty would long remain a "focus of tension," especially when it came to crimes committed by troops.