Peterson's conjecture on diagonal embeddings into ultrapowers of Haagerup factors

Let $N$ be a non-Gamma $\rm II_1$ factor with the Haagerup property. For an ultrafilter $\mathcal{U}$ on a set $I$, let $N^\mathcal{U}$ be the corresponding ultrapower, and let the diagonal embedding identify $N$ with its diagonal copy in $N^\mathcal{U}$. Peterson's conjecture. There is no property (T) von Neumann algebra $M$ embedded in $N^\mathcal{U}$ such that the image of $M$ contains the diagonal copy of $N$. This conjecture proposes a rigidity property for ultrapowers of non-Gamma factors with the Haagerup property; the supplied text records it as a question of J. Peterson and gives no resolution.