Proof, no, but they can make good citations (and often cite their sources, and these sources might come as close to proof as is practical.)

But all you've done here is show that, yes, there are some subsidies (which seem to mostly take the form of some favorable tax laws as I already suggested) but you haven't justified the use of the term "HUGELY subsidized" yet.

Even taking these figures at face value, and ignoring the gasoline/fossil fuels in general distinction ... $72B over seven years works out to about $10B/year. Considering just how massively gasoline is taxed -- the oil companies are taxed, gasoline itself is taxed by the federal government and the states, etc. -- these taxes are way, way bigger than $10B/year.

To be HUGELY subsidized (and not just somewhat subsidized) I'd expect more money to be given to the industry than extracted by taxes -- but the reality is quite different.

Ultimately, our government loves the fossil fuel industry, as it makes them a whole lot of money. Any subsidies (mostly tax breaks) our government gives are small compared to the benefits (i.e. money) our government reaps from the industry.

It's also not clear that we can take these figures at face value. For example, this article talks about how much of that $72B went to things that weren't related to fossil fuels.