I have never gone to the doctor when I had a flu. If it had lasted more than one or two days, or if I had a temperature higher than 102, then I would have gone. But as it was, nobody ever knew that I had the flu except myself and my family.
Even if I had wanted to go to the doctor for every time I got a flu or a cold, it takes at least a day or two to schedule a doctor's appointment. By the time the appointment had rolled around I would probably have cancelled, since the flu doesn't usually last very long.
This being the US, there are also a lot of uninsured people who can't go to the doctor even if they wanted to. For those people, Google is the only option. The CDC can collect as much data as it wants from the laboratories, but you can't collect what isn't there.
When you add in the uninsured people and the people who get better before visiting the doctor, it's not at all surprising that the lab estimates are 2x lower than reality. In fact, I would kind of expect them to be even lower than that.