Granted that's a selection bias: you likely won't hear about the cases where legit obscene output occurs. (the only notable case I've heard is the AI Dungeon incident)
TL;DR generative story site creators employ human moderation after horny people inevitably use site to make gross porn; horny people using site to make regular porn justifiably freaked out
Bring your popcorn
I feel like it would've been more than reasonable for them to have taken the position that the AI might output something distasteful, and implement a filter for people who were afraid of it.