Step 1: Check each statement against known mtDNA biology to spot the false one.
Step 2: The molecule is a small circular double-stranded genome, it is maternally inherited, and its mutation rate is high - all of these are correct.
Step 3: The mitochondrial genome codes for only 13 polypeptides plus its own rRNAs and tRNAs. The vast majority of respiratory chain subunits and other mitochondrial proteins are encoded by nuclear genes.
Step 4: Those nuclear-encoded proteins are translated on cytosolic ribosomes and imported, so the claim that all respiratory proteins are made inside the mitochondria is the exception.
\[\boxed{\text{All respiratory proteins are synthesized within mitochondria itself}}\]