Business that ship a lot (which is probably most packages) don't go to the post office for each shipment. Instead they buy machines/printers/software/labels which allows them to print off the correct label, and also combines all the money into something they handle the money in one larger transaction. There are lots of options in the above for different needs, if you a shipping a package even once a week you should look into them - often you get a discount for something that is easy for you to do (sorting outgoing mail by zip code saves them a lot of money and so they will pass that on to you)
Because there are so many options you can find one option and duplicate it easily enough and it will take them a while to catch it.
You ship something from, say, Pakistan. You pay them the postage, they put a label on your parcel, send it to the U.S.
The USPS receive it, label it, deliver it, and note that the original collecting agency was overseas.
Periodically, usually based on the inbound volume, they settle the net value with the other international postal union member.
So - you ship from somewhere porous, with poor systems, it gets delivered, originating agency says “not ours, not paying”, and the USPS is left holding the bill.
If that were the case the charges would be fraud and the victims would be the companies that paid for the postage. The charge of counterfeiting is pretty specific - if I steal a $100 bill from you and spend it I don’t get charged with using counterfeit money, I get charged with theft.