Most hospitals don't offer patient information online, but most allow people to inquire about patients over the phone. Various privacy regulations, however, limit what the hospital's staff can reveal, and patients can restrict what information the hospital staff can reveal.
Online databases are expensive to run, and there are no rules that require hospitals to provide online search tools. These tools could also run afoul of various privacy regulations. Hospitals are required to inform patients about what information callers can receive, and patients have the option to limit this information. However, hospital staff is responsible for deciding what information should be available if patients are unable to communicate their preferences. Rules require the hospital staff to make these decisions based on the best interest of the patient.