Well, I seldom wear out and about, I only wear outside of my apartment when I am heading to one of my ABDL friend's places. I also don't drive, I'm a commuter, I walk, take transit, it saves me money for babyish things, so I never get worried about winding up in a car accident padded. It also goes without saying that if I was ever mugged or arrested I probably wouldn't be padded, I never wear out and about late at night only during the day and once again, only on my way to friend's houses and I don't think I'd do anything that would merit a cop stopping me to ask a few questions or to pat me down on my commute.
Now the medical issue thing, that's a bit different. One time I was wearing on the bus to a DL friend's place and I got terrible motion sickness, it was also a very hot day, I very nearly fainted. After getting off the bus, I thought about what would have happened had I actually fainted. The thought of waking up in a hospital or on a stretcher after fainting with some AB brand diapers on was not a very comforting thought, it was absolutely mortifying, but fortunately, I didn't faint. Also, in hindsight, this fear was rather unmerited, I mean paramedics don't usually take your pants off when you faint now do they
I guess, bottom line, some people are more embarrassed and fearful of being caught rather than others in certain circumstances. My biggest fear when wearing diapers out and about is that someone picks up on the telltale crinkle or they see an elastic waistband poking up from beneath my pants and they decide to question me, or having a friend of mine who I haven't told catching a brief glimpse of some padding as I'm on the way to a friend's house.