Yes...we had to pay Germany to build a rifle....to kill Germans...
There were several cases of this happening around the world...I believe the British were paying the Germans to build artillery shell fuzes...
Kind of, but not really. Check the dates on those.
From what I recall of the last time I really dug into this, the ordinance bureau itself recognized that it was pretty deep into infringement territory and reach out to negotiate a settlement, which was resolved in 1905. Those royalties were capped and the payments wrapped up within a couple of years, well before WW1. It was all a pretty amicable process.
Things get more interesting later on, as DWM thought that the .30-06 cartridge was also infringing on their American patents for spitzer-type rounds. DWM approached in 1907 asking for a similar settlement, but the Ordinance Department's lawyers thought they had a stronger case and dragged things out for a few years in negotiations. Those negotiations fell apart in 1914 a few months before WW1 started and a lawsuit was filed.
The interesting part is what happened during the war. The lawsuit kicked around the courts until 1917, when the US got into the war, at which point the patents were seized as enemy assets. Since the government now owned the patents they got the case thrown out. A few years after the war DWM (or whoever inherited their patent portfolio, DWM corporate history gets a bit complex in the inter-war period and I'm not entirely sure who was doing what legally in the US during this time) filed another lawsuit alleging that the seizure of their patents had been unconstitutional. This was a much stronger case, the courts found in their favor, and they were awarded $300,000 in damages. There was an appeal which dragged out until the late 20s, at which point the government was ordered to pay, with interest, the original damage award. After interest it came out to a touch over $400,000.
So really it's more correct to say that we had to pay the Germans for a design that we eventually used to kill Germans, and then later on had to pay Germans after the fact for the bullets that we used to kill Germans.