not know any better は知識がない、事情が分かっていない、の意味。
0:53 from European settlers to today's American tourists which, if you didn't know any better, you might have mistaken Jenna and me for. もしあなたに(ジェナと私がテレビ関係者という)予備知識がなければ、ジェナと私を入植したヨーロッパ人やアメリカの観光客か、と勘違いされたかもしれませんね。
The Many Faces Of Jamaica
2:09 if I didn't know any better, I'd say you've been eating too much pie. もしも私がそれをキスのあとと知らなければ、パイの食べすぎと見ていたでしょうね。
Get your raggedy ass off my porch. 🥧 | The Help | Emma Stone | Viola Davis | Movie | Gaiman Global
0;30 she's 15. she doesn't know any better. 娘はまだ15歳で、右も左もわからない乙女だ。
Mom of Teen Who Ran Off With Teacher: I Could Have Stopped It
1:33 they don't know any better. 一般人は川の危険について何も知らないんだ。
7-Year-Old and 4 Family Members Dead When Tube Goes Over Dam