Can an insurer deny an entire fire claim because a homeowner cannot provide proof of ownership of some expensive items?

There is no general or simple answer, since  it  depends on the facts. In theory,  the insurer should pay on items where the existence, ownership, and value are all undisputed, even if there are some items that are not sufficiently documented for compensation. However, if the insurer believes that the insured is trying to defraud it--e.g. "making up" high-priced items for the claim--then the insurer may deny the whole claim and may be justified in doing so; trying to defraud  the insurer will typically relieve it of its obligations. There are attorneys who specialize in suing insurers and holding them responsible; if the insured believes the insurer had no grounds to deny the whole claim, he or she should consult with such an attorney.