Final answer:
The statement is false because riboswitches regulate gene expression by binding small molecules and affecting mRNA synthesis or protein synthesis, but do not directly cleave mRNA molecules.
Step-by-step explanation:
The statement "The riboswitch RNA becomes catalytically active to cleave mRNA only when bound to thiamine pyrophosphate" is false. Riboswitches are regulatory segments of RNA that can influence the expression of genes, but they do not directly cleave mRNA molecules. They can bind small intracellular molecules such as thiamine pyrophosphate to stabilize certain secondary structures of the mRNA molecule. This can affect gene expression by influencing the completion of mRNA synthesis or protein synthesis. However, riboswitches themselves do not possess catalytic activity to cleave mRNA; they act as regulators of gene expression by impacting transcription and translation processes.