A big reason Hindenburg burned up so quickly when it caught fire was because it was filled with hydrogen, a really reactive gas. Why didn't the German's use Helium over Hydrogen in order to improve safety?
Yes, it could have, and originally the designers intended to use helium. However, helium was a strategic material largely controlled by the US. The American government refused the sale of helium to Germany for use in airships due to the overt military use of lighter-than-air craft in WWI. The Helium Control Act of 1927 is the exact piece of legislation forbidding its export.
A lot of people talk about the strategic availability of helium in Germany, but there's also significant advantages to hydrogen.
I'll try to collect some sources when I'm on my computer, but this is all relatively common knowledge.
Firstly: hydrogen is cheap. Even if Germany had access to helium reserves, it'd still be very expensive.
Second: hydrogen is more effective. It produces more the lift per volume, which means an airship can carry less payload if using helium.
Thirdly, which is a combo of one and two: when an airship gains altitude, it has to vent gas to maintain ambient pressure. With hydrogen, they just vent it off. But because of the cost of helium, they instead under-filed the gas bladders so the helium could expand. This further lowered the lift capacity of helium airships.
Edit: accuracy and typo