This video, and the analysis from Emmanuel Saez and Gabriel Zucman which it is based on, is the subject of great debate. The best presentation of the arguments against their interpretation of the data, in my opinion, is given in this article by Matthew Yglesias. The whole thing is worth a read, but I'll just pick out one section in particular to reproduce here:
The headline fact rests on a bunch of assumptions
Treatment of the corporate income tax is particularly important for
this exercise because Congress enacted a big corporate tax cut in
Prior to that, the Saez/Zucman data shows the top 400 taxpayers paying
a lower overall tax rate than the top 0.01 percent or the top 0.1
percent, but a similar rate to the rest of the top 20 percent of the
income distribution and a clearly higher rate than the bottom 80
And this is important because, as first noted by libertarian economic
historian Phil Magness, changing how corporate income taxes are
handled makes a big difference in terms of assessing what rate the
richest Americans are paying in taxes.
The solid orange line represents the tax rates estimated by Saez,
Zucman, and Piketty’s scholarly article, using the assumption that the
burden of the corporate income tax is spread across all non-housing
capital (including small businesses and such), whereas the dotted line
shows the Saez/Zucman book’s estimates based on the idea that
corporate taxes are all paid by corporate shareholders.
Since ownership of corporations is very highly concentrated among the
richest people, if you consider a corporate tax rate cut to be a pure
tax cut for owners of tax-paying corporations, then you will get the
conclusion that the Trump tax cut was an incredible windfall for the
top 400 taxpayers.
On the right, it’s popular to argue the exact opposite of this: that
the economic burden of the corporate income tax falls largely on
workers and that Trump’s tax changes are a boon to wage growth. There
are well-qualified people with a whole range of views about this,
though as Saez and Zucman argue in their book, it does seem telling
that rich people tend to lobby loudly for corporate income tax cuts
and labor unions do not (if corporate tax cuts really do help workers,
unions should be the biggest champions for corporate tax cuts).
In any case, the shocking new fact presented in Leonhardt’s column —
that the very richest people pay a lower tax rate than the middle
class — is not just a result of policy changes but a result of changes
in how Saez and Zucman think we should understand the corporate income
tax, changes from their own work just a year prior.
Beyond those modeling issues, the income estimate for the top 400
taxpayers is not a direct measurement; the tax data necessary to
estimate their income after Trump’s tax cuts is not yet available from
the IRS. Instead, Saez and Zucman write in a technical appendix that
it “is based on triangulating publicly available sources and it could
be refined in future work” and they offer various hopes that more
precise estimation will be possible in the future.
To pile together several controversial assumptions, pair them with an
uncertain estimate relating to the wealthiest people, compile that
into a striking new fact that becomes the centerpiece of a media
rollout aimed simultaneously at promoting a popular book and
intervening in a presidential primary campaign — all this rubs
academic instincts the wrong way and helps explain a fair amount of
the scholarly backlash to Saez and Zucman.
The article also shows that the many different ways of producing these figures lead to very different conclusions: they cite this work by Gerald Auten of the Treasury Department and David Splinter of Congress’s Joint Committee on Taxation:
In conclusion, then, the figures & estimates presented in the video are based on significant assumptions on where the burden of payroll, sales, corporate, & even estate taxes fall, as well as a simplified view of the situation which ignores secondary economic factors, for example, the effect of increasing capital taxes. Given the disputed state of the available evidence, I don't believe currently there is sufficient evidence to confidently state whether or not we are not living under a flat income tax system.