I had a wender years ago made by a guy in Wurzburg/Wirzburg or however it was/is spelled. This type of furnishing (not the box but the furnishings and decoration) is apparently very typical to that area, I believe Bavarian?
There are a few different hypotheses one could come up with here. In no way do I think this is American, so I personally go into it with that perspective. I also don't think this is a particularly early piece and it very well may be 1770s or 1780s. By that point it is **possible** that an American rifle with a brass box had been viewed by the maker. It's also possible that this brass box was added later, again after an owner of the rifle had seen an American rifle with a brass box.
I suppose it's also possible that the gunstocker here just came up with this on his own, but given the absolute dearth of other German pieces with a similar setup, I find that incredibly unlikely. It certainly is very cool, whatever the story! Would definitely be interesting to really examine it in-hand.