c-hat MARK "known problems" - are model outcomes o

[Janet]

The MARK homepage states the following "known problem":

[i] "The deviance for the closed captures model divided by its degrees of freedom is not a valid estimate of c-hat. This problem carries over to the robust design model. I believe the problem is because these models are not in the exponential family, and this type of estimate of c-hat is only valid for models in the exponential family. This problem also extends to the robust design model".

Does this mean i) Closed capture modeled outputs for c-hat are wrong, or alternatively, that I shouldn't hand calculate based on deviance. Along this same line then, are the deviances correct in the modeled outcomes?
ii) My estimates of N using Huggins closed capture models have extremely large deviances and c-hats. As above, are these correct then?

Many thanks!
Janet