Borusyak, 2021 has a sentence

Third, in dynamic specifications, implicit assumptions about treatment effect homogeneity lead to the spurious identification of long-run treatment effects for which no DiD contrasts valid under heterogeneous treatment effects are available

In staggered DiD, I understand that the dynamic specification is to use the leads and lags in a model to capture the dynamic of treatment effects.
I also understand treatment effect homogeneity is a disadvantage of standard DiD in staggered laws implementation cases (rolling-pout event dates) because it does not account for the heterogeneous effects during the treatment onset.

I understand that "spurious relationship" is

The spurious relationship is said to have occurred if the statistical summaries are indicating that two variables are related to each other when in fact there is no theoretical relationship between two variables
But I do not understand why homogeneous treatment assumption leads to "spurious identification of long-run treatment" in staggered DiD as quoted in the above sentence. In large, I did not catch the theme of the sentence in this paper

Third, in dynamic specifications, implicit assumptions about treatment effect homogeneity lead to the spurious identification of long-run treatment effects for which no DiD contrasts valid under heterogeneous treatment effects are available.