In my family, we usually would go in to see the doctor if the progression of the illness was getting worse. Influenza usually comes on very strongly and knocks you out for a week, but the worst days are the first and second, and then you're just on bedrest for a while. Same with most illnesses. It's when you feel sick and keep getting sicker that it's time to see a doctor.
It sounds like that's what the family in the article did: when her illness got worse, she went to the doctor. But the doctor just diagnosed her with the flu and sent her home, so it's not like it helped.
[1] http://www.merckmanuals.com/home/infections/viral-infections...
The decision on how bad you feel is Emergency Room $$$$$, Urgent Care $$ or Doc visit $. Also just because you pay more doesn't mean you get in either, I've been stuck at Emergency Room for 12 hours before.
Urgent care clinics are similar but more mini hospitals - hence the '$$'.
It is uncertainty in costs just as much as the costs that keep people away from doctors here.
The cold or flue lasted 9 days, with fever coming and going, we took her one day to the walk-in clinic. I understand they don't want a million children collapsing the system but let's say I wasn't happy.