Not true. I just placed an order with two add-on items (totaling $7) and one non-add-on item ($20). The two add-on items were shipped separately.
Also, I'm pretty sure everything that's actually sitting in an Amazon warehouse is prime-eligible. The stuff that isn't is the stuff going through 3rd party sellers that don't use fulfillment by Amazon.
The intent is for add-ons to ship in a box with the main Prime order. This doesn't always happen due to the combination of what you order and the locations of the items across Amazon's fulfillment network. When this happens Amazon is eating the cost of those extra shipments and is considered a 'miss' by the inventory folks.
Everything in the warehouse is not prime. If fact, an item can flip from prime to not prime in near real time if the most accessible inventory is used up and all that is left is the stuff in the 'reserve' areas of the warehouse. This is the area where the giant boxes of inventory stored. Grabbing inventory from there involves pulling it down, opening, pulling apart eaches, and then stowing in fast access areas.
Also, I'm pretty sure everything that's actually sitting in an Amazon warehouse is prime-eligible. The stuff that isn't is the stuff going through 3rd party sellers that don't use fulfillment by Amazon.