Influenza is not a 'mild' disease, although most people do recover fully from it, and its course is well recognised and described. If someone has diagnosed influenza but recovers fully over a mere couple of days, their flu infection has very clearly been considerably modified by pre-existing immunity - in the poster's case quite likely by vaccination - or by fast effective treatment such as Tamiflu. It is not, in that case, a full blown case of influenza, or 'flu proper'.
There is a common misconception among the public that flu is just like a bad head cold. Nothing could be further than the truth. There are so many misconceptions around flu and flu vaccines that at this point it's beyond a joke. At least we don't seem to be seeing specific anti-flu-vaxxers (yet!)