I do hate it when people don't know when they're wrong.
Yes, Apple pays next to nothing on a large portion of its revenues. Look at all the foreign revenues that are funneled through Ireland at next to no cost (which is what that article was about). And the numbers I found for Apple's total tax were a tad lower, 22%-24% or so. In fact, average effective US corporate tax rate is around 21.9%, which is just above that of France and Germany, and not far off the global average of 17.4% (Source:http://www.actontaxreform.com/wp-content/uploads/2016/09/International-Comparison-of-Effective-Corporate-Tax-Rates_FINAL_20160926.pdf. And no, I'm not cherry-picking that data. I'm using the best available. The rest of the figures are for stated rates or non-adjusted rates)
Now, as for payroll taxes and such, you have a point - but are still wrong.
(Source: http://www.oecd.org/tax/tax-policy/tax-database.htm#C_CorporateCaptial)
Comparing 1965 to 2015, total tax revenues went from $167,022 million to $4,754,120 million - an increase of 2,746%. Corporate taxes went from $27,390 million to $395,888 million - an increase of 1,345%. During that time period the statutory tax rate decreased from 46% (or more....could only go back as far as 1981) down to 35%. The corporate tax as a share of total revenues decreased from 16% to 8%. So where was this increase in tax revenue mainly placed? On workers.
Average hourly wage in the US for regular workers increased from $2.50 an hour to $21 an hour over the same timeframe - an increase of 740% (Source: https://fred.stlouisfed.org/series/AHETPI). But their share of total gross domestic income has been decreasing, from 49% to 43% (Source: https://fred.stlouisfed.org/series/W270RE1A156NBEA) What's driving this? Higher income tax burdens.
Let's compare some numbers. As I stated, salaries increased 740%. Total tax revenues increased 2,746% and corporate tax revenues increased 1,345%. Individual taxes increased 3,564%, from $52,894 million in 1965 to $1,938,111 today. Personal tax has risen from 31% of the budget to 40%. You are correct that social security has increased - 4,973% from $22,192 million to $1,125,923 million, in fact! But the burden for this increase is larger on the employee (5,807% increase) than on the employer (4,317% increase). Capital gains has seen the largest increase over this timeframe, 6,901%, but is still laughably small at $174,550 million.
Now lets compare to Ireland, home of the lowest tax rate in Europe. Let's see where it got them. 1965 - Irish tax base of a whopping $317 million. Corporate tax of $29 million, 9% of total. After they invented themselves into a tax haven, tax base of $60,356 million (growth of 778%), corporate tax revenue of $6,873 million (growth of 993%), 11% of total revenues.
To me, that's not impressive. The growth rates are much, much lower than that of the United States. The percentage of total revenues isn't much different from the United States. Ireland needs these rates because without them, they don't have jobs, and jobs is what they care about. US has no such need, really, because this fear of inversions is completely overblown.
The total number of corporate inversion in the past 35 years is??? 50. Overwhelmingly in pharma and finance - the two squeakiest clean of industries in the country, as far as ethics goes. (Full list here: https://www.bloomberg.com/quicktake/tax-inversion). Rules can be put in place to stop these easily enough, and most keep their employees in the US anyways, so the loss is only of the corporate tax, not all the other benefits. (Also, TIL Tim Hortons is owned by Burger King, and was originally a US company)
So, in sum, corporations are not paying enough. Their profits are growing faster than wages are growing, while they're pushing the tax burden for the country off themselves and onto workers in various ways. Either jack up the corporate rate or jack up the capital gains rate, but something has to be done.