The Economist is based in the UK, so they know with absolute certainty that the rich most definitelly do not "pay for everything" since in that country, much more than most, the industry for Tax Avoidance and Evasion is MASSIVE, using British Crown dependencies (like the Channel Islands and the Bahamas) and even supported by the local legislation (such as their very special Non-Resident Tax Scheme which actually applies to people resident in the UK), all of which expensive enough that they're only worth using for people who make millions per-year.
The idea that a British-based magazine specialized in Finance and Economics are unfamiliar with the kind of schemes used by the likes of the Duke Of Westminster to avoid paying any tax at all and instead think the rich pay most taxes beggars belief.
At best, the Middle and Upper-Middle Class pay for everything. De facto the rich pay less effective tax on their incomes than the lowest levels of the Working Class, some even in absolute terms (as admitted by none other than Warren Buffet when he said that "I pay less tax than my secretary").
I read The Economis for over a decade until the 2008 Crash (when I finally saw the disconnect between the ideas they claimed to defend and the actions they actually approved of, and thus stopped reading it) and I have no doubt in my mind that this is just their usual "opinion forming" mix of half-truths, cherry picked factoids and pseudo-Scientific theories knowingly built on top of lies.