Basically the conversation was about how technologies are always demonized and like the argument that the internet is ruining people's attention spans, Pinker noted that people initially demonized reading and writing because they thought 'if you just write down everything then you won't train you memory to remember things'
Any truth to this? either by the Romans or any civilization?
I don't know what Pinker might have been referring to, but I suspect if anything it is not to Romans or a civilization in general but Socrate's famous argument against writing. Socrates essentially argued that reliance on writing and reading as a form of learning would displace memory, that writing will make people think they've learned something when they really haven't, and that people will overvalue the written word as a potential source of truth.
This is just one of Socrates' views (and of course we have his views in the first place because someone other than him wrote them down). It was not a dictum by an entire civilization. And one should avoid making this sound like writing was a "new technology" at the time; Socrates lived around 300 BC, writing was invented thousands of years before that. To think about this in terms of "technology" is not quite in the spirit of Socrates; he is talking about practices of the mind.
Plenty of others wrote things down; if they didn't, we wouldn't have the records of them today.
An aside: none of this should imply that Socrates was wrong, or that technologies don't come with serious tradeoffs, including to memory, attention-span, misinformation, etc. And the fact that people criticized technological changes in the past should never be taken as an indicator that one needs to be uncritical of them in the present — that is just bad logic by itself. There is a form of fallacy that goes along the lines of: "someone in the past once suggested X was not an unambiguous good; since their argument did not carry the day, we should never criticize X, Y, or anything else going forward." It is very silly and yet I have seen very well-educated people make it as if it were persuasive, notably in the area of technological enthusiasm (where the Luddites get denounced, for example, for correctly recognizing that automation was dramatically disrupting their economic livelihoods). When automobiles were introduced, people against them argued they would kill lots of people. They were right (30,000 a year in US alone, to say nothing of the long-term effects of gasoline addiction, car-based city planning, leaded fuels, climate change, etc.)! That we still live in a world dominated by automobiles doesn't disprove that, or mean we can't say similar things in the future about other technologies.