The article concluded that vinegar is an inexpensive, non-toxic, biodegradable antimicrobial, but that it is not as good as commercial cleaners.
Vinegar contains about 5% acetic acid. The article said that this acid kills bacteria and viruses, and suggested that the effect was probably brought about by denaturing the proteins and fats. If proteins are denatured (their shape and hence functionality changed) the bacteria may no longer be capable of growth. I'm not sure that the rate of fat trans-esterification would be very high, but it might contribute to damage of the microorganisms.
The action of vinegar on bacteria is quite interesting. Strong acids completely dissociate into ions. For example, hydrochloric acid dissociates into hydrogen and chloride ions. These particles carry a charge and cannot enter the bacterial cell through the cell membrane.
Weak acids, such as acetic, citric and ascorbic acids, don't fully dissociate; in solution, a significant proportion of the acid remains undissociated and therefore uncharged. So for acetic acid:
CH3COOH ⇔ H+ + CH3COO-
This is where it gets interesting; the weak acid solution outside the cell has a moderately low pH, which keeps a proportion of the weak acid in the undissociated form (the equilibrium is driven to the left). The uncharged molecule can pass through the cell membrane into the cell. Here it encounters a higher pH (the interior of the cell is closer to neutral pH) and so the equilibrium is driven to the right and more hydrogen ions are produced. These ions interfere with the cell proteins and hence cell metabolism, since many cell proteins are actually enzymes. The cells are either slowed or prevented from growing. A multipurpose cleaner favoured by my wife claims to "kill 99.9% of germs" ***. The active ingredient is 3.2% citric acid.
However, the Fact Buster authors also consulted an infectious diseases specialist, Professor Peter Collignon, at the Australian National University. He made the point that concentration on disinfection is the wrong emphasis. Thorough cleaning would practically remove the need for disinfection in many cases - remove the dirt and you remove practically all the bacteria. Disinfectants may not penetrate a layer of dirt or the slime produced by a bacterial biofilm. The film may actually neutralise the disinfectant by reacting with it.
The priority should therefore be to remove dirt and bacteria and only then apply a disinfectant if it is required.