No, it is not true because it is worse than that.
Christakis and Fowler have analyzed a huge data-set (study) of 12,067 people assessed repeatedly from 1971 to 2003 as part of the Framingham Heart Study. The results:
“if a friend of yours becomes obese, you yourself are 45 percent more likely than chance to gain weight over the next two to four years.”
However, if a friend of your friend becomes obese, gaining weight is about 20 percent” and with regard to a friend of the friend of your friend obesity, it is 10 percent more likely. In other words:
“Your friends make you fat, but so do their friends, and so do their friends of friends.”
It seems to be related to norms. With your friendship circle changing, your mind-set of an acceptable body size and your behavior change, too.
friend smokes, 61% higher chance of becoming a smoker
friend of your friend smoking, 29% higher chance of becoming a smoker
friend of a friend of friend, 11% percent higher chance of becoming a smoker
Similar results showed their study on happiness:
“if your friend of a friend of a friend is happy with their life, then you have a 6 percent greater likelihood of being happy yourself. Now six percent might not seem like much, but consider that other studies suggest that if I gave you a $10,000 raise, that would only trigger about a 2 percent increase in your happiness.” (Medium).