If an application has been started without a splash screen and in a headless system, both assertions are applicable:
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public static SplashScreen getSplashScreen()
...
    Returns:
(1) [...] null if there is none
    Throws:
        [...]
(2) HeadlessException - if GraphicsEnvironment.isHeadless() returns true
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With current specs an implementation is free to implement (1) or (2) behavior. That's an ambiguity.
It should be clear from the text that HeadlessException is thrown in headless systems regardless the splash screen absence/presence.