What is the contradiction between the White House's position and Elon Musk's portrayed role in federal agency layoffs?

The White House maintains that agency heads, not Elon Musk, are responsible for decisions about laying off federal workers, creating legal protection for these layoffs. However, this contradicts how Musk has portrayed his role. While the White House claims Musk is only serving in an advisory capacity, Musk has publicly conveyed that he and his team are personally responsible for the layoffs. This contradiction has led to about a dozen lawsuits against the Department of Government Efficiency (DOGE), particularly from employees who have been terminated through unexpected badge confiscations or access revocations.