Physical/SRB measures without slow recurrence

Let the hypotheses and conclusions of Theorem~ and Theorem~ be understood, including their physical/SRB measure conclusions and slow recurrence assumptions.

Physical/SRB without slow recurrence conjecture. In Theorem~ and Theorem~ the slow recurrence conditions are superfluous.

If true, this would show that the existence of physical/SRB measures depends only on positive Lyapunov exponents and not on slow recurrence. The source does not state a resolution.