I'm having trouble grasping the difference between the --heterozygosity and --input-prior options in GATK's GenotypeGVCFs tool and how they affect the QUAL scores that are emitted.

I'm specifically wondering what is meant by the statement "There are instances where using this prior might not be desirable [...] as for example when the ancestral status of the reference allele is not known." in the docs for the --input-prior option.

If, as the documentation says, P(AC=0) = 1-sum of input (where the input is the unfolded SFS), then isn't it still assuming that the reference allele reflects the ancestral state? I feel like the only way to avoid this assumption about the ancestral status of the reference allele would be to supply the folded SFS, which isn't an option.

And finally, how is this truly any different from what --heterozygosity is doing to calculate P(AC=0)?