It’s definitely possible to go three days without taking a shit. I’ve had to do it before. I was a 45 minute drive away from the nearest gas station, and the only available toilet within walking distance was an outhouse that was infested with yellowjackets. By the end of the third day, I was considering digging a new outhouse.
I don't think I've talked about this in the last 10 years or so. Even I had forgotten about it till now. In primary school, I had a friend who would challenge me with things. We'd see who can finish a Popsicle first, or who can run faster, mostly stupid innocuous stuff. One day he challenged me to hold off poop. We'll see who gives up first. Now, back then I only pooped like once every 2 days or so. I thought it won't be a big deal and I'd win easy. But days go by, he claims he still hadn't pooped. Well, I didn't wanna lose, so I didn't poop either. It ended with me having extreme stomach pain, and finally giving in on the 8th day. I ended up seeing a doctor as the pain won't end. My parents were really angry with me when I told them what had happened. (They didn't know I was doing this. I'd go into the toilet, sit a while, flush, and come out. I knew they won't let me do it otherwise.) Then they went to talk to his parents. Turns out that bastard had given up on the second day! We're still in touch, but never did any challenges after that.
It’s not even always that bad, I’ve gone a week and a half before, could’ve gone longer but I forgot my lactaid at home. It’s just genetics and training how long you can hold it. These days I regularly go more than 3 days, usually twice a week.
It's honestly very possible depending on the setting. I've gone over two days before without really realizing it while camping. Part of it is just not eating that much, part of it I think is some subconscious desire to avoid shitting in the woods or in an outhouse. But I've had it happen multiple times where we go camping on a Friday night and I realize late Sunday that I never went.
I realize that's not the same as three full days, but I have to think if I was intentionally eating very little it would be attainable.