Hey H.!
Our son (also 3) also complains that he's "too busy" to go potty. You're right - playing outside or watching a favorite show is far more important. :)
Although we haven't had many accidents because of forgetting, we have lots of close calls. We did a couple of things - we started watching him closer. If he grabbed at his crotch or danced around, we sent him to the bathroom. If he was "too busy" we'd offer to remove the distraction (take toy away, turn off show) or he could go potty & come back to the activity. He doesn't like having things taken away, so he'd go potty. We also "offered" to buy more diapers. He absolutely loves his big boy underpants, so he didn't want diapers again at all.
We never let him think it was okay to wet his pants, but really don't shame him either. I think it's all the tone of your voice & your body language. I let him know it's not a big deal to change/wash the clothes, but it's a drag when you can't wear your favorite underwear/shorts/pants because you peed on them. I remind him that it takes less time to go potty than it does to change clothes (get back to show/playing/whatever faster).
We always try to follow up with a "next time let's try really hard to remember to potty right away - I'll help you remember!" It seems to work, but he does regress when he's tired, hungry, grouchy, learning something new... Times like that I just remind myself there aren't many kindergarteners in diapers. :)
Good luck!
J.
Mom to Chase (3)