I can maybe understand the logic of this. Sugar is a natural preservative, e.g. take preserves such as jams and marmalade, sugar stops bacteria and moulds growing in the product, so it stands to reason it might hinder the bacteria somewhat and allow the antibiotics to be more effective.

A spoonful of sugar can help beat bugs: Antibiotics made more effective by glucose

It seems a spoonful of sugar can do more than help the medicine go down – it can also help make it work.
Sugar can improve the effectiveness of antibiotics against infections, according to researchers.
They found that glucose and fructose – types of sugar found in plants – make bugs that cause chronic and recurrent infections more vulnerable to drugs.

Sugar can improve the effectiveness of antibiotics against infections, according to researchers

Such infections often occur when bacteria ‘shut down’, making antibiotics ineffective against them.
Over time, the bugs, known as ‘persisters’, return to life, causing patients to relapse.
The scientists, from Boston University, tested the effects of drawing the bacteria out of their hibernation using sugar.
They found stimulating the bugs with sugar renders them vulnerable to antibiotic attack.

Testing the strategy on Eschericia coli (E. coli) bacteria, a common cause of urinary infections, the researchers were able to eliminate 99.9 per cent of persisters in just two hours.
Without sugar, the drugs they used had no effect, according to a report in the journal Nature.
The team now plans to investigate whether sugar additives can help fight tuberculosis.