@Cassiespark is spot on. Your box has to be 1 cubic foot (or 1728 cubic inches) or less. It does not matter how you get to that 1 cubic foot. Anything over that is considered dimensional weight, and an additional charge
may apply, if the dimensional weight cost is greater than the actual weight cost.
I assume with the new company they require a photo of the package. If so, I suppose the MSC could look at the package photo and know if one side is greater than 12" and not accept it based on that, though it would be difficult to tell 15" from 12" in a photo, as an example. It still does not impact how USPS handles it. As long as it is less than 108" (length + girth), a package can go Priority Mail.
There is the truth.
Then there is the right thing to say.