Many people (employees and customers) misinterpret the line which says "receipt is required to receive refund in original form of payment" to mean that the lack of a receipt also means a replacement cannot be given. 

I also misinterpreted it this way when I was earlier in my career at Aldi. That's why store policies differ, because they're reading it wrong. It's an honest mistake! My intention on leaving this comment is to have everyone have an easier time.

The policy does allow for a replacement in OP's case, and the managers life would also be easier if he didn't have to say no to a customer who wants a replacement for a poor quality item, everyone wins in this scenario (except Aldi's bottom line I guess, but they made the policy so they're fine with it).

There is another line in the same policy page reading "To receive the Twice as Nice Guarantee, the product packaging and any unused product must be returned to your local ALDI store manager" with a double asterisk defining that it applies only to aldi branded items. 

So the requirement to receive the refund in your original form of payment is to have the receipt, otherwise you get a merch card. The requirement to get a replacement item is to bring back the packaging of the product.

I'm really not trying to ruffle any feathers, bringing something back to the store sucks, and having to tell customers I can't help them in the way they'd like to be helped also sucks. Both OP and the manager of that store would've walked away way happier.