Statements like "X is can be used to represent any program/function, therefore it is all we are every going to need" are pretty silly.
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I regularly do see this claim verbatim, with Turing-completeness being used as "proof". It's not a straw man, it's a surprisingly common position. Before RNNs were cool, the "universal approximator" argument was being used in the same way to say that NNs were sufficient for AGI.
Mostly, it seems like an excuse to avoid having to think about what (R)NNs really do, and where their limitations lie.
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I think that is fair to think in that case.
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