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I'd say the correct statement would be that a tuned absorber only traps the frequency it's tuned at.
It's an obvious deduction that harmonics will most likely be attenuated as well but that should not be considered axiomatic.
Simplest opposite scenario is a room with dimensions A x 2A x C where one dimension is twice the other. Killing the 2A mode will not do anything for the A mode as there is a separate "source".
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