It is generally true, most corporations pay around a 17% tax rate; however, it is wrong to assume that many of them should be paying a 35% tax rate, considering that: 1) The US Corporate Tax Rate is progressive, just like other income taxes in the US and 2) very few corporations actually make enough income to pay a 35% corporate tax. There are more than 6,263 thousand registered domestic Corporations in the United States. The the highest marginal tax bracket is 35% on anything above $18,833 thousand. Very few corporations make over $18.833 million dollars, let alone $15 million, which would be a 38% tax, plus a $5,150,000 tax on top of that.
If anything, majority of corporations (which would be 1120 and 1120S) make less than $100,000, which would put them anywhere from a 15 - 34 percent tax bracket.