Correct. If they're not living with you, then they need their own account.
And of course you intentionally gave you word, unless someone forced you at gunpoint to click "I agree" when you signed up for the service. If you failed to read what you were agreeing to you, that doesn't mean you aren't responsible for abiding by it. If that were the case, then you can tell your credit card company that you don't owe them any interest or late fees because you didn't read the card agreement. Come on, you know that's not how it works.
A vague social media post does not constitute a legally binding agreement of any sort, so it's irrelevant. You're grasping at straws here.