BS.
I just ran the numbers. Do it yourself, if you'd like, on any number of websites. $50,000 income, married, filing jointly, two children as dependents, standard deduction only. Total tax owed: $2690. If both children are eligible for the standard child tax credit, the amount owed would be $690.
To promote this story line, ABC used a filing status of either "Single/Married Filing Separately" or "Head of Household" and ignored tax credits, which would yield taxes of $3985 or $3398, respectively.
Never mind how much each and every one of us pays when we buy a product or service created under a 34% corporate tax rate. Taxes are passed on to the consumer so a change from 34% to 9% is a savings, not directly but, indirectly seen at the register.
You are right. The devil is in the mathematical details which a mathematically illiterate society will reject just as they have rejected all other of our attempts to introduce flat taxes. They can even figure out that the millionaire pays more taxes on a ten percent flat tax than does the guy making $30,000 on a ten percent flat tax.
These discussions and debates are best had outside an election - in the halls of power where, presumably, people who can do math, can debate it. Progressives will always reject a flat tax, not because it is unfair, but because they use loopholes to buy power and control behavior.