Q: Can we refer to a possessive noun by a possessive pronoun?

for e.g. The public's opinion lie in its inherent misconception about the judgment.

Yes we can

yes.

although ... not the other way around (the dreaded 'possessive poison' rule - which is so completely unimportant that, although cited by gmac, it has never been the deciding factor in any official problem). if you have any trouble with that rule, i suggest that you forget all about it, because the odds that it will ever actually decide the correct answer to a problem are infinitesimal.