You would be quite wrong. If you count all taxes, rather than cherry-picking the most progressive ones, the top 20% pays about 2/3rds of all taxes. They also earn about 2/3rds of all income. The total tax rate in terms of all tax paid divided by income earned is remarkably flat: the bottom 20% has an effective rate of about 20%, and the top 1% has an effective rate of about 34%.

See: http://ctj.org/pdf/taxday2015.pdf