According to this page on the nLab, it is currently unclear whether or not the entire Yoneda lemma generalizes to $(\infty ,1)$-categories rather than just the Yoneda embedding. Have there been counterexamples to the stronger statement? If not, what complications are there in generalizing the entire Yoneda lemma? The whole lemma is a very powerful tool in ordinary category theory, and if there is no definitive answer, are there any reasons to believe that the generalization should or shouldn't be true?

By the "entire" Yoneda lemma, I mean the isomorphism $F(X)\cong Nat(h_X,F)$

According to this page on the nLab, it is currently unclear whether or not the entire Yoneda lemma generalizes to $(\infty ,1)$-categories rather than just the Yoneda embedding. Have there been counterexamples to the stronger statement? If not, what complications are there in generalizing the entire Yoneda lemma? The whole lemma is a very powerful tool in ordinary category theory, and if there is no definitive answer, are there any reasons to believe that the generalization should or shouldn't be true?