Frankly, accounting is so old that it might actually be true. Also, it depends on what is meant by "trade": individuals exchange goods between themselves in a free-form setting, like as in sharing a bite off each others' meals or lending each other stuff. But in order to reliably and repeatedly exchange goods through time without any suffering through systematic losses - which is more like the problem of a shopkeeper - people are pretty much required to keep some form of running tally of their previous transactions in order to know what they've done so far and what their bottom-line is.

It's very much like saying that there would be no traveling without maps (or perhaps without navigation). At a glance, it is wrong. But it seems a fair and reasonable statement if it's interpreted as if saying that if people had no way of telling where they are or at least where they're going, then there would be no way of "traveling" from or to anywhere. There would merely be wandering.

In contrast to the other commenter, I don't think it's overstating things. In my opinion, it's understating things. Accounting was the killer app for writing things down back in the earliest historical times. Many clay tablets in Akkad are about accounting, and the earliest Phoenician records were accounts as well. The more familiar will recognize that it is the Phoenician alphabet that evolved into most of the Mediterranean world's alphabets, including Latin, Greek, Cyrillic, Hebrew, and Arabic script.

So arguably, without the need for accounting, writing, would have been invented far later, and the literature that we have from ancient times would have been lost to oral tradition.

It's glib, but justifiable. Though it's slightly overstating and oversimplified.