What are our rights if we relied on information provided by an insurance claims adjuster that was incorrect?

You can still honestly give a sworn statement about the discarded items, as long as you don't make anything up;  you can give your best estimate about what each of those items was worth, as long as you say it's an estimate.  One easy way to do this, is put an asterisk ("*") after each estimated value, and then, at the end of the list, the asterisk followed by something like, "Estimated value.  Item previously discarded on instructions of ________ company adjuster ________."

You will usually not have problems from a proof of loss, as long as you don't make any knowingly false statements.

Will out the form too the best of you knowledge, with whatever documentation you may have of value (e.g. any old receipts? credit card statements with lost items charged on them? etc.) If the company dispute the value, you will stand on the fact that their agent, for whom they are legally responsible, told you to throw the items out. If you have evidence of that--such as any correspondence, emails, even notes you took at the time or the names of other people she told that to--provide copies of that information, too.

Legally, a business is responsible for the actions of its agents in the course of their employment. If the insurer does dispute paying you the full amount and also will not stand behind its agent's actions, you option is to sue. Before doing that, you will need to weigh the cost of the lawsuit (legal fees, etc.) and the fact winning is never a given or guarantee vs. how much more you are hoping to get, to make the right decision as to what to do.