It's not a misconception just not a 100% rule.
I have high blood pressure and can't fix it with diet and exercise either, was underweight and a runner, now healthy weight yoga & lifting, have been vegetarian and omnivore, it doesn't affect it at all. Drugs work so I take them. But it's also true that people who are fat or inactive can reduce their blood pressure and blood sugar by getting in shape, it is usually a lifestyle thing.