The trouble is we often misinterpret our little ones knowing where to go, as knowing when to go.
If he can play in a playground with poo in his nappy, or even manage to squeeze one out while he is playing then perhaps he doesn't understand the signals his body is telling him about when to go until it is too late to communicate that he has to go. That's not something he can easily control, and he isn't developmentally ready at 3 to realise pooing and weeing in nappies is giving him his sore bum, even if you tell him. There's a cognitive dissonance.
We all have a sense of interoception, and for some people it is hypersensitive and for some people its hyposensitive.
When you're focused on doing something else, maybe something more fun and exciting it can be really hard to listen to your body. A bit like when you are watching tv and eating dinner and suddenly realise you've eaten too much and feel bloated, because your brain was too preoccupied on something else.
The trouble is that as a 3 year old with a new found independence, the world is a lot more exciting, so it can be harder to listen to what your body is telling you, that might be when to eat, when to drink, when to go to the bathroom. Sometimes visual reminders can help, like visual time tables or even just having the potty in his line of site at all times.
Because of that new found independence though he will also be developing a sense of privacy and that can make using a potty even harder because they're usually where you can be seen. Finding a quiet corner in the room can really help where you can still be aware of the general area but not making solid eye contact.
His sore bum might also be giving him some anxiety about pooing, and to poo he might need a familiar feeling which is his nappies. It takes time to build that trust up with the toilet that is bigger, louder and wetter, a completely different feeling, and requires you to be stationary when you just want to be on the go all the time.
Tomorrow is a new day.
Although I personally didnt gain much from contacting ERIC, I do think they may be able to offer some insight, and they are very good at coming up with solutions to try so I do recommend giving them a call before you do anything.