I am confused by a statement in the very classical paper of A. A. Albert "On the construction of Riemman matrices II", Ann. Math. 1935, Thm 16. If I understand what he saying, the theorem says that given a quaternion algebra $D$ over a totally real field $F$ of degree $t$ over $\mathbb{Q}$, which is not split at any of the infinite places of $F$, there exists an abelian variety (over $\mathbb{C}$) of dimension $n$ with endomorphism ring (tensored with $\mathbb{Q}$) equal to $D$ if and only if $n = 2tr, r>1$. (I changed the notation slightly).

Now, I thought that such things existed even with $r=1$. For example, if $t=1, F = \mathbb{Q}$ one can have an abelian surface ($n=2$) with endomorphism ring $D$. Another place where these things are alluded to (for arbitrary $t$) is a paper of Y. Morita "on potential good reduction of abelian varieties" J. Fac. Sci. Univ. Tokyo, 1975, remark 3.1.

I guess my questions are, first is whether Albert is right, wrong or misunderstood by me. In case Albert is wrong, is there a place where examples with $r=1$ are constructed? Can every such $D$ occur , when $r=1$?