It used to be the accepted view that in Greco-Roman antiquity reading was normally aloud -- I've never heard this view applied to any society in the modern era, so I'm guessing this is what your source was referring to.

But it's not true for Greco-Roman antiquity either. Almost the whole of the argument that reading was always aloud in antiquity depends on a single late passage, in Augustine's Confessions 6.3, where Augustine describes intruding on Ambrose's reading and sitting in silence, and pondering Ambrose's motives for sitting in silence so long and wondering why he was reading to himself. This is not only a misreading of the Augustine passage, it also neglects literally dozens of much older pieces of evidence on the subject.

However, the counter-argument wasn't put together until 1997, so if you found this in a source written before that point, the author shouldn't be censured for being wrong -- just out-of-date. Here's part of an old thread that goes into details. As far back as we can look, there are many more references to reading that imply silent reading than those that imply reading aloud. Some of them are as explicit as the Augustine passage. The problem that has kept Augustine at the top of the citation list for so long is that the Greeks in particular routinely used metaphors of "speaking" and "hearing" for what texts say.

Here are the earliest relevant references, all from the fifth century BCE:

• Euripides, Hippolytos 856ff. - Theseus opens a letter to "see" what it "speaks" to him; a few lines later (and there's no evidence that he leaves the stage) he cries out at its horrible contents, stating -- using the aural metaphor -- "it shouts, it shouts". At 882 he cries, "I will no longer keep this unspeakable story within my mouth's gate".
• Euripides, Iphigeneia at Aulis 34ff. and 107-108 - Agamemnon reads and edits a letter repeatedly, but a slave standing next to him still doesn't know its contents.
• Herodotos 1.123-125 - Cyrus is alone, so the references to the letter "saying" things and Cyrus "hearing" them are the aural metaphor again; cf. an inscription "speaking" in Hdt. 8.22.
• Aristophanes, Knights 115ff. - Nikias gives Demosthenes a bundle of oracles to read, and Demosthenes is so absorbed in reading them that when Nikias asks him what they say, he says "pour me another cup of wine". A few lines later he paraphrases what's in the text without quoting it directly.