All optometrists are allowed to perform invasive eye surgery.

The statement that all optometrists are allowed to perform invasive eye surgery is false. In general, the scope of practice for optometrists varies significantly by state or country, and while some optometrists may receive additional training and certifications to perform certain types of minor surgical procedures or laser treatments, not all optometrists have the legal authority or training to perform invasive eye surgery.

This limitation ensures that only those optometrists who meet specific training requirements and who are licensed by the appropriate boards are permitted to undertake surgical interventions. Therefore, it is clear that the claim that all optometrists can perform these procedures is inaccurate, leading to the conclusion that the correct answer is indeed that the statement is false.