Alternating double-zeta reduction conjecture

Let $m$ be a positive integer, and let $\zeta(\overline{r},s)$ denote an alternating double zeta value, while a non-alternating double zeta value has no barred index. Alternating double-zeta reduction conjecture. The combined sum

$$\zeta(\overline{2m},2)+2m\zeta(\overline{2m+1},1)$$

can be expressed in terms of non-alternating double zeta values.

This conjecture predicts that a particular family of alternating double-zeta combinations reduces to non-alternating values. No proof or resolution is supplied in the excerpt.