A couple of points.
First, "those in the top 1% of earners, pay about 40 percent of all taxes", tells us nothing about whether or not, on average, they are paying their fair share. If their income is more than 40 percent of all income, they are getting off light and not paying their fair share, and if it is less, they are seemingly paying more than their fair share
from a pure percentage standpoint. However, the more one has, the higher percentage of one's income one can afford to pay. If, for example, one has only enough money to buy the minimum necessary of food and shelter and clothing for survival, then one has no money that one can afford to pay in taxes, whereas anyone making more than that can afford to pay some money on taxes or something else. And the more one makes, the higher the percentage of one's income there will be that is surplus.
(To make this clearer, let us pretend that it takes $10k to barely live [the number selected is purely arbitrary; pick any number you want, and adjust the following incomes by the same percentage]. Anyone making $10k can afford to pay nothing extra, so they can afford to pay 0% of their income in taxes or anything nonessential. Anyone making $20k can afford to pay 50% of their income in taxes and nonessential items, since they, too, only need $10k to live. Anyone making $100k can afford to pay 90% of their income in taxes and nonessential items, since they, too, only need $10k to live. See the pattern? The more one makes, the higher the percentage of one's income that one can afford to pay in taxes and other such things.)
So looking at the matter from a pure percentage standpoint is unfair from the start, as the lowest income earners cannot afford to pay anything at all. (The simplistic use of percentages, by the way, is typical of the kind of fast one rich bastards try to pull on people to con them into thinking the rich are not really the cheating bastards that they are.
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Second, what the "average" of a group of people does tells you practically nothing about any individual in the group, so the whole thing is somewhat pointless and silly. This is true of other things as well: If you know what the average height of a man is, what does that tell you about the height of a particular man? Whether the average millionaire is a cheating bastard or not will not tell you anything about whether or not a particular millionaire is a cheating bastard.