I need to know if I understand this point.
The factor of HZZ vertex in the SM Lagrangian is half the value of the Feynman rule which appears in Diagrammatica.
When I calculate the decay of Higgs into 2 Z, I have to integrate over only half the phase space, because the two Z's are identical.
So, at the end, I get the same result as if I took the exact Lagrangian factor and integrated over the entire phase space, i.e. $2\cdot0.5=1$.
But, in the second way, I would in fact do two mistakes which cancel each other and accidentally get the correct answer. Is this correct?