Perfectly true - in the US and Australia the majority of what they sell is sourced, produced or manufactured in those countries. Switzerland is somewhat different having adopted much of the EU legislation and regulations, (including Schengen and the free movement of people).
I'm not of the...
The only reason Aldi and Lidl can operate in this country and easily import food, (and export cash), without additional tariffs is because we are members of the EU.