Sometimes when I'm riding, I'll see another cyclist by the side of the road, obviously repairing a flat tire.
I can identify - I used to do that a lot myself. On a couple horrible days, three times in a day! (That will make you want to hang up the bike!) Thankfully, since I switched to Vittoria Randonneur tires, my flat quotient is WAY down. I haven't fixed a flat so far this year.
Years ago, I was a "professional" bicycle flat-tire repair instructor. Well... "professional" may be a stretch, but over the course of 2 or 3 years I taught a one-hour Community Education class. Probably 25 or 30 people learned the art of flat repair under my expert tutelage. (You can definitely save some cash... I understand most bike shops don't patch tubes, but rather replace them. My personal policy is - 3 or 4 patches, then the tube gets replaced.)
Whenever I've been repairing a flat enroute, I've always thought it was VERY nice when a passing cyclist asked if everything was OK, and I generally try to do the same thing, or at least make sure they're equipped with what they need, to get the job done.
If the flat-tire victim has his bicycle turned upside down, I tend to dismiss that person as an "amateur." Is that wrong? Do y'all turn your bikes upside-down, to fix a flat tire?
I used to, years and years ago (probably 1000 flat repairs ago! haha). But I observed, and learned from practice, that it's at least as easy to separate a wheel from a bike by lifting the bike... and that keeps your saddle, brake hoods, handlebar tape, bike computer, etc., from getting scuffed up in the dirt.
Nowadays, if you see me fixing a flat tire, my bike will be lying on its side, or leaning against a support... or after the third flat in a day, maybe crumpled in a heap where it landed after I tossed it! (Just kidding about that last one. As much as I've felt like it a time or two, I've never tossed my bicycle.)