I have tried 1) pasting the "embed tweet" code into the "insert link" option, 2) pasting the "embed tweet" code into the body of my post, and 3) I've even tried posting the "embed tweet" code into the "image URL" option.

I've seen people successfully embed tweets in their posts on here...I WANT TO BE ONE OF YOU!

ETA: TyrannosaurusBataar answered my question! YUSSS!