How you interact with them is the key to 90% of what your child learns from you. You’re already participating in their viewing. Use this as a stepping stone for dialogue regarding plausibility, and demonstrating critical thinking.
“Do you agree with that influencer? Why or why not?”
“What are the influencers motivations?” Dazzle them with possibilities they had not considered too.
“If I told you I’ve been to space would you believe me? But I’m your parent! Why is my claim beyond belief?”
“Can you verify what that person is telling you through reliable means? This is how I would do that”.
… and so on. Just do more of what you’re doing and up the investigation portion IMO. Don’t be afraid to learn something yourself while they witness it. Just be careful to avoid arguments as they’re getting to that age…