The only solution is to avoid buying processed meat products. Buy meat in its whole natural form. The supermarkets should know where their products come from, there should be traceability for all the products they sell.
This incident certainly isn't Aldi's fault, but it's likely to hurt them in the long-run. I'm not a fan of Aldi in general, a lot of their brand things taste nasty to me, but I wouldn't let this stop me from shopping there if I did. Partially because it isn't on them and partially because I don't eat any sort of meat to begin with. It just doesn't affect me!
The nearest Aldi's to me is pretty far away so I don't shop there and now I'm kind of glad I never made it there. I'm adventurous at restaurants and have tried unusual meats, but when I go to the supermarket, I want to know what I'm buying. I guess we can't really control the content of our burgers unless we hand the butcher some meat and watch him grind it up.