The couch and TV remote have killed many times more people than cycling, running or swimming ever will.
I have a horrific family history of early cardiac disease, disability and death. I was also obese through most of my childhood, adolescence and young adulthood and continue to struggle with my weight. I took up cycling as running was too hard on my ankles and knees and, though still a clyde, have lost weight and gained fitness. Despite this I had two heart attacks, each of which required a stent to be placed. I've had more than one person say something along the lines of "See, all that bike riding didn't do you a bit of good. You still had a heart attack."
Whole truth be told, genetics set me up for early heart attacks from the start and I didn't do myself any favors in my younger years. Even if I had been more health conscious, I probably would have had one or more heart attacks at some point, maybe not quite as soon. The interesting fact is, that while cycling didn't prevent my heart attacks, my cardiologist credits being an avid rider with my rapid and complete recovery, and perhaps even saving my life. He is impressed that I suffered no appreciable damage and have a cardiac ejection fraction that is in the high normal range. I walked out of the hospital in two days and was back to work without restriction in two weeks (the shortest time allowed). He told me to keep cycling as much as I wanted and his wife rides with my cycling group and has been on our Tour de Cure team. If it's good enough for my cardiologist and his family, it's good enough for me.