Leigh Ishikawa's presentation on 'Establishing an Agile Testing Culture' emphasizes the necessity of integrating agile practices into every facet of an organization, rather than mandating it for specific teams. Key points include the importance of hiring the right talent, fostering a supportive environment for testing, and understanding the unique culture of a company before implementing changes. Successful agile organizations prioritize people and iterative improvements while aligning with the agile manifesto.