I wouldn't be very surprised if it was. In the history of mankind, the ability to sustain something as big as a culture by purely plant-based means would not be the easiest way of doing things and unless there exist strong outside pressures (such as ethical ones that can be seen nowadays) then plant-based diet would be overshadowed by more diversified sources of nutrients. From the very beginning, human species sustained on a combination of animal (hunters) and plant (gatherers) food. Generally, for a change to happen, there needs to be a reason for the change. As it happens, there just never was a sufficiently big one for cultures to do differently.
It is also good to note that plant-based diet has some specific requirements such as cobalamin (B12) which are hard/nearly impossible to get from plant-based diet alone and need to be supplemented. While this fact would be unknown to the civilizations that we are talking about, the simple correlations would probably be apparent over time, where people eating only plant-based diet would suffer from B12 defficiency symptoms (fatigue, depression, reduced mental capabilities, even psychosis).
The only real source of outside pressure for most of our history as species would be probably religion or a supreme ruler with plant-based agenda in mind. No religion with impact that spans cultures that I am aware of requires people to follow plant-based diet and I have not heard of an authoritarian figure who would require this either. In the case of the supreme ruler, the diet would be hard to control anyways and it would be probably overruled as soon as they die so we are talking about a horizon of one human lifetime at most.
Plant-based diet is a viable diet for a great number of people in today's world and can theoretically be means of sustaining a culture. This has, however, not been true for most of our history and so I think the claim that you refer to is true. I would be happy to be proved otherwise if someone can offer a counter example.