Your assumptions about the inner workings of Selenium may have been correct for Selenium RC, which was a JavaScript-based technology used in Selenium 1.0. Being entirely JavaScript-based, however, meant that it was limited to the browser's JavaScript sandbox, which precluded some actions in the browser.
Selenium 2.0 introduced Selenium WebDriver, which is a different paradigm of web automation. WebDriver attempts to model the user experience and actions as closely as possible. Since modeling the user experience dictates certain design and technology choices for interacting with elements, it likely won't work if the browser is minimized, since a user cannot interact with the page while the browser window is minimized.
Incidentally, I'd be surprised if finding the elements was the issue with executing WebDriver code. Interacting with the elements found, like attempting to click on them or send keystrokes to them, I would completely expect that to fail.