[jwmhjwmh]

Similar to the second quote, English speakers nowadays (at least where I live) say things like "I have the flu." In this phrase, I believe "the flu" refers to the ailment in general as opposed to what affects the speaker in particular. Maybe this is also the case with your second quote?

[alisonkisk]

I have the coronavirus. I have Covid.

I have a headache and a toothache.

I have a cold and a fever. I have yellow fever.

I have a cough. I have whopping cough.

I have the flu.

I have the chicken pox, smallpox, the measles, and the mumps. I have rabies.

[CRConrad]

Why is this flagged; WTF is there to flag about it? The commenter obviously isn't claiming to have all these ailments at once!

They're illustrating how different diseases take different articles (or none at all) in standard English usage.