How much packaging do you seriously use with other brand names on it? Are you dumpster diving at retail chains where they have branded packing materials?
It’s one thing to reuse a box from a MFG, but to use a box from another retailer that can confuse the customer quite a bit.
I think you can continue re-using packing materials, just don’t use retailer-branded packing materials unless it is from Amazon.
Amazon, though it has many sellers, wishes to present a homogenized identity, which is something that helps their business. You are putting your own interests above Amazon’s, which may make Amazon rethink their relationship with you.
Most customers that buy on Amazon do not even realize that often they aren’t buying from Amazon directly. When you send their Amazon order in an ebay box, that is confusing and something Amazon would really hate.
The safest thing to do is to not re-use any branded materials. This is what I do.