Veterans' Emergency Care Claims Parity Act This bill modifies certain deadlines for the submittal of claims by a non-Department of Veterans Affairs (VA) individual or entity seeking reimbursement for the provision of emergency treatment to a veteran. Specifically, a non-VA individual or entity seeking such reimbursement must submit a claim not later than 180 days after the treatment was provided. (Under the VA's current policy, such claims for unauthorized emergency care must generally be submitted within 90 days for conditions that are not service-connected and within two years for conditions that are service-connected.) Veterans may not be held liable for payment if a claim was submitted by an individual or entity after the deadline due to an administrative error made by the individual or entity or by the VA. The VA must publish information regarding emergency care authorization for non-VA providers on a publicly available VA website.