They try to cut out as many layers of middlemen as possible, and then act as a reliable partner (they pay in full, on time, every single time and never make a supplier refund them for unsold product).
In the case of your avocados, they're probably buying them directly from the farmer:
> When you partner with ALDI you can expect simplified processes that give you more time to invest in your business, while receiving high-volume, timely orders that allow you to plan ahead.
> Prefer to work directly with manufacturers or growers [1]
By having a really low range of inventory and really high turnover of that inventory so they focus on bulk buying only a few items. Walmart sells everything and there is a cost in supporting being a one stop shop. In Aldi it's typical to have 1 type of smoked back bacon for example while Walmart might have 10 types of smoked back bacon.
How are they able to do this across so many food categories? The interview doesn't answer this question.