I didn't think so, either, but the dems use the terms subsidy and tax break interchangeably in this report. They're playing Merriam-Webster to present an issue as they want it viewed.
Subsidy was a term used by Pelosi, Chris Van Hollen (D) Maryland and the reporter.
I hate to agree with Pelosi and company, but I believe that the term subsidy is correct. The break stems from the fact that the oil companies are allowed to drill on federal lands. They pay royalties for drilling rights. Clinton (Yes, this was a Clinton program) tried to encourage oil companies to continue drilling for oil here in the US, back when oil prices were very low, and drilling in the US wasn't as profitable as obtaining oil overseas. The royalty payments were decreased or eliminated on a certain amount of oil. (not sure which) Now that the price of oil makes it profitable to drill in the US, the dems want to eliminate the royalty break or subsidies. I don't believe it has anything to do with taxes, which I know the oil companies still pay plenty of.
I don't know enough about oil economics to know how this all plays out, but to me it seems like changing the royalty structure now, after the companies have committed to drilling costs and resources is unjustified. Its like luring people to a community with very low tax rates, and then, once they have all moved in, raising them higher than the other communities in the area.