Is there ever a possibility of false diagnosis of pulmonary fibrosis?

Yes, very common. Pulmonary fibrosis is a loose term which is sometimes used by mistake for idiopathic pulmonary fibrosis (ipf). I see numerous patients who are told they have pulmonary fibrosis who have normal lungs.
Maybe. Pulmonary fibrosis is often a diagnosis made on clinical history, exam and chest scan findings with pulm function tests. If a biopsy is done of the lungs then this greatly increases the chance that the diagnosis is accurate. Without a lung biopsy the diagnosis may be less accurate.