Helen, you are right. When I read the article, it just sounded like the idea was for everyone to run. Certainly it is something that must be worked up to for any person out of shape.
It just kinda got me that in one point it says to start slowly and in the next it's run here or run there. And to me that says that the writer has not had the issue of not being able to do those things described. Some people must lose weight before they can even think of being active with their family (especially without making their family slow down for them) or even running (whether for fun or for a race).
A person with the right kind of mindset can sign up for a race (walk/run or just run) and become highly motivated to prepare, lose weight, and finish, and you have proved you are one of those people.
I would just feel stupid for trying and give up without much effort. I know plenty of people who would never be up for a competitive sport (and who would view a race as completely competitive rather than just as a positive experience).
I would guess that most doctors would not encourage their obese patients to sign up for a walk/run race at the very beginning of a weight loss program. It could certainly kill whatever motivation is already there because it is seen as too difficult.
With enough motivation and hard work, anyone can incorporate running into their routine, its a matter of time and patience (just like anything else with weight loss).