Yes, these actually regional products do exist, but unless there is further information on the product itself there is no chance to know what that “regional part” may be: the (processed) product itself, the raw materials, the packaging? Any of these three allows retailers to label them as “regional”, which is a shame.

Example from Rewe:

It states “Aus Niedersachsen” (“from lower Saxony”, which is a German state) but this may be only where the product was packaged. Without looking at the label there is no chance to determine if the pickles are from Niedersachsen. It could be the case (the label on the right side says “Gewürzgurken aus ?”), but you have to check each product one by one. And you have to do this check every time because this can change for each batch at any time. So it is easy to mislead consumers here.

Edit:

The country of origin is only required for certain goods anyway: Eggs, fresh fruits and vegetables, honey, and some more. (german source). Also under some circumstances there needs to be clarification regarding the products origin, but that is not the case in general.

So this is what you get for years of conservative, capitalist lobbying.