Just want to address the " re- boxed" thing. Companies don't usually buy a packaged item and take it out of the package and put it into their packaging. That would be expensive and have many health code issues. The most common thing is - a factory makes a product and puts it in different boxes, wrappers, etc depending on which company is buying it. Sometimes, a factory might sell large lots of something - like a tanker truck full of processed milk - to be packaged at the companies factory.
I just posted on another thread about Aldi today .Their gluten-free products, the ones I bought are all certified gluten-free, From what I'm reading on the packages, they do not process on shared equipment. Someone got an email back from Aldi on the other tread on this topic.
It doesn't address the labels but they did get a response. With the holiday weekend, it might take a while for them to catch up. It also appears that these products are reboxed gluten-free products from other companies that do have info. Check out the other thread.
I don't know a lot about Aldi, but I believe they are a large, international chain. It is possible they have their own factories and large contracts with other manufacturers.
To further explain- there is a margarine factory here. They make the same margarine but it gets put into different wrappers and then boxes depending on the retailer that is buying them. They make a brand name and a several store brands.
Looks like one branch of Aldi owns Trader Joes, too.
"Aldi mainly sells exclusively produced, custom-branded products (often identical to and produced by major brands"