Secondly, I don't see how "non gaap accounting" is relevant when the claim is that they are audited by an independent entity using standards which are not under their control.
Here is the link to the statement from the Post Office: http://about.usps.com/news/statements/080117.htm
"By law our competitive package products, including those that we deliver for Amazon, must cover their costs. Our regulator, the Postal Regulatory Commission (PRC), looks carefully at this question every year and has determined that they do."
Suppose you have a store that sells rutabagas and phonebooks. You buy at wholesale prices of $1 per rutabaga and $2 per phonebook. You need a markup to cover the cost of rent, bond payments, volcano insurance, and heating oil. You could mark up each product by 50% or by $0.75 or whatever. You can do the same percentage, the same per-item amount of dollars, the same amount of dollars for the total of all items sold, or something else. If you sell rutabagas for $1 each and phonebooks for $5 each, does that count? You didn't exactly take a loss on the rutabagas, but on the other hand they didn't contribute toward paying for that volcano insurance. Maybe selling the rutabagas cheaply will bring in more customers, many of whom will buy overpriced phonebooks. If a rutabaga sold at $0.79 causes an average of 3.14 phonebooks at $8.05 to be sold, does that rutabaga cover costs?
I suppose I agree that it's not easy to attribute costs, but if this is a defense of Citibank or Trump's claims about Amazon, it seems like special pleading. If it isn't so easy to determine if costs are covered, and if the Post Office is not giving them any deal other major shippers don't get, and they are audited according to some standards that people defined as acceptable, then it seems as though people should stop claiming the USPS is subsidizing Amazon.
If I estimate cost A is $1 and cost B is $2, I'm going to say that my estimated average cost is $1.50, not $2
As far as required profitability, as any non gaap accounting numbers can attest, you can make anything look profitable if you meddle with the numbers long enough.