In at least one way, they may be right. It's one of the few dietary choices that has a long enough history for real data to exist, and an analysis of seven clinical trials and 32 studies published from 1900 to 2013 in which participants ate a vegetarian diet, and in which differences in blood pressure (BP) associated with eating a vegetarian diet were measured, found that eating a vegetarian diet was associated with a reduction in the average systolic (peak artery pressure) and diastolic (minimum artery pressure) BP compared with eating an omnivorous (plant and animal) diet.
Writing in JAMA Internal Medicine, the authors note that, in the 32 studies, eating a vegetarian diet was associated with lower average systolic and diastolic blood pressure, compared with normal diets containing meat.
Obviously there could be other factors. If you undertook a vegetarian diet for health rather than cultural reasons, body weight, physical activity and alcohol intake, which also play a role in the risk of developing hypertension, could be much different than other people also. Still, dietary modifications have been shown to be effective for preventing and managing hypertension and a vegetarian diet could be the way to go.
“Further studies are required to clarify which types of vegetarian diets are most strongly associated with lower BP. Research into the implementation of such diets, either as public health initiatives aiming at prevention of hypertension or in clinical settings, would also be of great potential value,” they conclude.
Citation: JAMA Intern Med. February 24, 2014. doi:10.1001/jamainternmed.2013.14547