What legal basis (if any) might the billed party have for challenging such cases?
None. Under the conditions stated, the customer owes the full amount of the bill.
Companies often forgive these bills for (what I assume are usually) PR- or cost-related reasons,
Lurking in the background is bankruptcy. You can't collect $1,000,000 from someone with only $100 of assets that are exempt from creditors and a minimum wage job.