Observing the age of the Universe when orbiting a black hole

Imagine a civilization developing on Planet X that is orbiting a black hole (or a similar gravitationally massive object). Given the time dilation near such a massive object, do the inhabitants of Planet X measure the age of the universe incorrectly? Does the universe appear much older for them?

As a follow-up question, is there a way to measure the age of the universe independently of the observer's circumstances? What about the extreme (and unlikely) case of a planet which is surrounded by black holes?

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Observing the age of the Universe when orbiting a black hole

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