Step 1: The question asks for the FALSE statement about Corynebacterium diphtheriae.
Step 2: Diphtheria toxin production is NOT chromosome mediated. The gene encoding the toxin (tox gene) is carried by a lysogenic bacteriophage (beta-phage). Only strains lysogenised by this phage can produce toxin, so the statement in option A is FALSE and is the correct answer.
Step 3: The pathogenicity of diphtheria is almost entirely due to the exotoxin, not local invasion, so damage by toxin production (option B) is TRUE.
Step 4: Diphtheria toxin inhibits protein synthesis by ADP-ribosylation of elongation factor 2 (EF-2). The organs most affected are the heart (myocarditis) and nerves (demyelinating neuropathy, palatal palsy), so option C is TRUE.
Step 5: Clinically diphtheria is classically a disease of unimmunised children, so option D is TRUE.
Conclusion: The single FALSE statement is that toxin production is chromosome mediated, hence the answer is option A.