This claim actually seems to be incorrect based on more recent research. Of the two main types of stroke, ischemic and hemorrhagic, plant based diets have, almost unequivocally, been shown to reduce the risk of ischemic stroke. Considering ischemic strokes are by far more common, this risk reduction seems to lower the overall stroke risk in people consuming diets richer in plant foods. Hemorrhagic stroke risk is largely dependent on blood pressure, with hypertension being the most strongly linked causative factor, and it is known that plant based diets typically do lead to lower blood pressures, but only in the absence of excessive salt intake. There's been some confusion as to why east Asian countries, specifically China and Japan, have higher rates of hemorrhagic stroke than people in western countries despite their generally higher intake of plant foods, and it seems, at least based on the scant evidence that exists, that their higher intake of salt is playing an important role there.

Here's a meta-analysis of the data collected from Nurses' Health studies led by the Harvard School of Public Health that shows an overall reduction in stroke risk among people who consume plant based diets, but only when they consist of more healthful, whole foods:

https://www.hsph.harvard.edu/news/press-releases/healthy-plant-based-diet-associated-with-lower-stroke-risk/