The Germans "payed" for their war effort by enslaving and murdering millions of people and systematic pillage.

In the 20th century, during a war economy, money loses its importance as a measure of value of goods. The reason is basically that centralized rationing and allocation replaces a normal market economy for many things. You can't buy a set of tires, a liter of fuel, or day's worth of food just because you have the money, you also need a ration card or government permission to have or consume these things. This is even more true for large business, who were not free during wartime to just buy inputs and start producing goods, they had to get permission from the government in the form of allocation of raw materials and labor. Additionally, almost all prices were fixed by governments. That doesn't mean money was totally discontinued, it still existed but it became largely peripheral to the main sectors of the economy.

Now, on to Germany specifically.

Did Germany have access to international credit. No they did not. Even earlier in the war and before the war, Germany was largely isolated from the international finance and trade economy. If they had trade agreements, they tended to be negotiated bilaterally in a kind of barter system because countries tended not to trust each other's currency in the late 1930s and Germany was particularly untrustworthy in its use of currency.

Production numbers that we have were mostly NOT falsified, although sometimes figures are misleading or incorrect, it's not a widespread issue. Most of the statistics were compiled post-war when there was less propaganda value from any falsification.

Lastly, it should be mentioned that in 1942-1944 systematic pillage and slavery were prominent features of the German war economy. Large amounts of food, goods and raw material were by force (and sometimes fraud, i.e. "paying" for things in devalued currency) imported into Germany to feed the Nazi war effort. Additionally huge numbers of people were conscripted for labor from occupied territory and moved to mines, farms and factories inside and outside of Germany and worked under harsh conditions and minimal food rations, resulting in a heavy death toll. This is the basis for the German production numbers in the war years, it wasn't some miracle of technology or finance.

The main source for this is Adam Tooze's "Wages of Destruction" but it relies on some other material for the second paragraph.