Well, sort of like my SIL, your idea of "offensive" is very different than mine. Now, OTOH, I don't always ask a health question, but he was coughing so heavily, wife and I both wondered. Since the Pandemic, and even before, it just seems like a lot of folks go out for a meal or shopping sick. If we are in a grocery store and hear someone coughing or wearing a mask, we get out of that aisle immediately. Now, how do you feel about hearing someone, most likely a young guy, sitting at a table next to you, and dropping the F bomb a lot while talking to others at his table? Do you want to say something to him? I remember, years ago, I was at lunch with a lady friend and the people at the table next to us were cussing like mad. My friend looked over and said "I came here with my friend for a nice lunch, not to hear the garbage taking you are doing, so please stop." Guess what, they stopped the cussing. As for a person telling us "fighting a cold for 3 days", we would immediately ask for a TO-GO box, pay and leave. Actually we done that once. We had already ordered our dinner and an older man behind my wife was coughing a lot. When our food came, was ask for TO-GO boxes, paid and immediately left.
This reminds me of a fight I had in a restaurant 55 years ago over 'supposed' foul lango.. My first cousin and I were sitting at a booth enjoying a conversation about the Atlanta Ryheim Section concert we had went to 'Champaine Jam' in Atlanta. A young couple seated at booth behind us got offended by the word 'bugger' I had used referring to a band member. I said, "he was a cute little bugger". He jumps up with a mean look on his face, said 'you need to watch your filthy mouth', we're trying to eat" I impolitely told him ," I'm not talking about the buggers in your nose, I was talking about a cute little drummer". He then told his wife, whatever, to beat my ass. She got up and I told her what was going to happen. First off, I'm going to let you pass the first lick so best make it a good one, then after I stomp your ass, you're going to jail for attacking me. Now go sit down and don't listen to him. She slapped the heck out of me and my prediction came true, the people sitting around saw her slap me and they told the police how it happened. I was raised part time in the woods in a family brothers, male cousins, only 2 other girls were several years younger, so boys were all I had to play and fight with growing up.
My mother was British. I use the word "bugger" all the time. I say that people get things "buggered up." I also see people light up a fag and eradicate a spelling error with a rubber. I wonder what those folks thought you meant. They'd get really offended if I asked if they wanted me to knock them up in the morning...the silly little buggers.
LOL, I think he was just in a bad mood and took it out on Mary 'my cousin' and I. John, speaking of incorrect spelling, I spelled it wrong, it was booger, like in the nose. I like British humor; I watch them on YouTube sometimes reacting to our food or music. You ever do that?
You sound like a GA gal alright! My dad used to say, "Now baby, don't go starting any trouble. But be sure to finish it."
Yes we did learn how to protect ourselves, huh? I won't talk about the one I lost,  She was from Georgia too.
I can't fathom asking a coughing stranger at a restaurant why they were coughing. Lots of folks cough frequently, especially during the winter. I always cough in my elbow and face away from others. I see most folks doing the same thing with little kids an exception. Most restaurants have tables or booths separated enough so coughing shouldn't be an issue. I am more concerned that the cooks are sanitizing their hands frequently or table service is using clean rags and bleach solution to wipe the tables, but I will never asked. I go out to eat for enjoyment and seeking conflict or personal invasive discussions, just isn't my thing. If I ever get paranoid about others coughing in public, I will stay home.