I think the language contained in the logs would be enough. Not everyone in Starfleet's linguistics division is as ignorant of Romulan as Uhura's predecessor.
But what possible reason would the first Nero encounter give to anybody for thinking that the language they hear is Romulan? According to the "three dialects" scene, the language Nero would have spoken would have been Vulcan! (Unless, of course, he spoke English to his Starfleet captive, or used a superior future translator that would leave Robau hearing English but unable to deduce the originating language.) There's no good reason why Starfleet would think that Vulcan-looking (if bald and tattooed) people speaking Vulcan would be Romulans, not unless something like "Balance of Terror" subsequently happened.
And obviously something did, because our heroes in 2258 know a thing or two about Romulans, none of which they could have learned from the stories of late Robau's surviving crew. But with some other
incident revealing that Romulans are renegade Vulcans, everybody would naturally realize that the renegade Vulcans who destroyed the Kelvin
were most probably Romulans.