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I think OP is talking about the fact that it is possible to represent and transmit sound via an electromagnetic medium and that therefore this limit is not a limit on sound information (which is nothing but generic information that can be transmitted at the speed of light) but rather a limit on sound as it occurs physically (in the way that you've described).

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The key word there is “represent”. Radio isn’t sound. If I make a recording and mail it to you, the delivery time isn’t “the speed of sound through the mail”.

You can get into a whole thing about trees falling in forests and how a pressure wave only becomes sound when it’s interpreted as information, but that’s totally irrelevant to an experiment about pressure waves through a medium.

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