Final answer:
The false statement is that binding of sigma causes RNAP core to bind tighter to non-promoter sequence.
Step-by-step explanation:
The false statement regarding how RNA polymerase (RNAP) interacts with promoter DNA versus non-promoter DNA is binding of sigma causes RNAP core to bind much tighter to non-promoter sequence.
The correct statement is that when the sigma subunit binds to the core RNAP, it reduces the affinity of the RNAP core for non-promoter sequence and increases the affinity for the promoter sequence. Option D is false because the binding of sigma subunit does not cause the RNAP core to bind tighter to the non-promoter sequence.
Therefore, option D is the false statement in regard to how RNA polymerase interacts with promoter DNA versus non-promoter DNA.