You need to read and understand the FMLA law itself to see why doctors are not filling out FMLA paperwork. CFR 825.113 specifically says that certain conditions (the common cold, the flu, ear aches, upset stomach, etc.) do not meet the definition of "serious health condition."
I believe the actual wording is "normally" do not meet. These rules are written for the average worker. The conditions mentioned can affect a pilot. For a pilot, some of the conditions listed can induce vertigo which is serious in my book. Go to your AME, and not your normal Doctor.
You also have to look at the definition of "continuing treatment" 825.115 were you will see that in most cases where we cannot fly i.e. cold, sinus infection, etc. (viral infections), bed rest, fluids and off the shelf meds are not continuing treatment.
The language also includes taking a prescribed course of medication as a "continuing" event. Most Doctors will prescribe antibiotics even with a viral infection to prevent a secondary bacterial infection. Antibiotics meet the standard for treatment of continuing nature. Don't make it too complicated. Go to your AME.
The doctor has to certify on the FMLA paperwork that you meet the criteria of a serious illness and are receiving continuing treatment for said illness. If you do not meet those qualifiers and the doctor fills out the paperwork anyway they are abusing the FMLA system. My doctor will not fill out FMLA paperwork for this reason. The law is cut and dry. A lot of doctors abuse this unfortunately.