Equal complementary-tuple degrees conjecture for balanced multipartite hypergraphs

Let $H$ be an $n$-balanced $r$-partite $r$-graph, and let $I$ be a subset of $[r]:=\{1,2,\ldots,r\}$. An $I$-tuple is an element of $\times_{i\in I}V_i$, and an $I^c$-tuple is defined using $I^c:=[r]\setminus I$. For tuples, let $d(\cdot)$ denote degree in $H$. Equal complementary-tuple degrees conjecture. If

$$d(e)=d(f)$$

for every two $I$-tuples $e,f$, and

$$d(g)=d(z)$$

for every two $I^c$-tuples $g,z$, then $H$ has a perfect matching unless $r$ is odd and $n$ is even. The conjecture proposes that uniform degrees on both complementary tuple classes force a perfect matching, apart from the stated parity exception. The source describes this as a bold conjectural weakening of the Brualdi-Ryser condition; no resolution is supplied.