Only if the original manufacturer does the shipping, which is not always true. If it says "prime" it's warehoused by Amazon, original manufacturer or not, and subject to commingling.
> "sold and delivered by TheOriginalManufacturer"
It's commingled if it says "sold by TheOriginalManufacturer, delivered by Amazon"
It's a pretty small line next to the price.
(Prime delivery tag isn't an indicator btw, sellers can get prime certified and still handle their own shipping.)
Kinda a stretch to say it's a minority though. There wouldn't be such an issue with counterfeit articles from Amazon if it wasn't the norm