Linear isoperimetric function for universal covers of generalized Dehn complexes

Let $X$ be a compact $2$-complex with the generalized Dehn property, and let $\widetilde X$ denote its universal cover. Linear isoperimetric-function conjecture. Then $\widetilde X$ has a linear isoperimetric function. This would extend the classical implication from the Dehn property to linear isoperimetry to the generalized Dehn property; the supplied text gives no resolution status.