My nose/sinus/throat is all very sensitive to perfumes and aerosols these days, and even if it's not strong enough to close my throat up and choke me, it still tends to make me feel sick. I've not used any spray and rarely any smelly stuff for over a decade.
Most soaps and some shower gels are fine though, so there's no problem with starting a day "clean".
On the morning train, you can normally smell people who use deodorant instead of washing. It's quite hard to describe - air freshener in a festival toilet? Artificial sweeteners on a stilton cheese? Anyway, if their perfume isn't strong enough to physically harm me, I don't care.
I used spray deodorants as a teenager, and unscented roll-ons for many years after - but after stopping using it, I found, like the couple you mentioned, that I didn't sweat as much, and the sweat that was there didn't smell as bad. Oddly enough, anecdotal evidence suggests my natural smell increased my attractiveness quite significantly. Of course, all of these may have just been coincidental factor of age/hormones/circumstances etc though.
I was a bit paranoid for some years, and always asked/checked with trusted people "do I smell?". I found I can smell myself when I do.
My work is sometimes quite physically demanding, so during the ~two months a year when it's potentially warm (Northern UK), you can get a bit sweaty - but so is everyone else. If you really feel the need, a quick armpit wash in a sink at lunchtime, or a "festival shower" with a wet-wipe would sort that out.
Anyway, so the rough answer is "There is less body odour. You get used to what's there. Most of it smells quite pleasant, sometimes even to the extent of it being animalistically magnetically attractive"