The technical eligibility requirements for Medicare coverage in a Skilled Nursing Facility (SNF) are indeed precise and play a critical role in ensuring that beneficiaries receive the necessary post-hospital care under Medicare Part A. Here's a detailed explanation based on the criteria you provided:

1. Enrollment in Medicare Part A with Available Days: Beneficiaries must be enrolled in Medicare Part A, which covers hospital insurance and some post-hospital care in SNFs. Furthermore, they must have days left in their benefit period to use for SNF care. A benefit period begins the day a beneficiary is admitted as an inpatient in a hospital or SNF and ends when they haven't received any inpatient hospital care (or skilled care in a SNF) for 60 days in a row.
2. Three-Day Prior Qualifying Hospital Stay: Before SNF admission, beneficiaries must have a qualifying hospital stay of three consecutive days or more, not including the day of discharge. This requirement emphasizes the necessity for care to be an extension of treatment for a condition treated during the hospital stay. The three-day hospital stay rule is essential as it ensures the beneficiary's condition is severe enough to require skilled nursing care, which can't be provided at home or in an outpatient setting.
3. Admission to SNF Within 30 Days of Hospital Discharge: Beneficiaries must be admitted to an SNF for covered services within 30 days of being discharged from the hospital or another SNF stay. This condition ensures continuity of care and that the SNF services are related to the condition treated during the qualifying hospital stay. In specific situations where immediate SNF care isn't medically appropriate, the 30-day window can be extended, allowing beneficiaries to access SNF care when it becomes necessary within a predictable timeframe.

These technical eligibility requirements ensure that Medicare Part A covers beneficiaries who need skilled nursing care following a hospital stay. The intent is to provide necessary skilled care that can only be safely and effectively performed in an SNF setting, ensuring that beneficiaries receive the appropriate level of care for their recovery.

Understanding these requirements is crucial for healthcare providers, beneficiaries, and their families to navigate the Medicare system effectively and to ensure that those who need SNF care can access it under their Medicare Part A benefits.