As a pure numbers game "average % paid" is a bit misleading. What the "average person" would pay would be the median % paid. Average does tilt the total upwards because the wealthy (who pay more) are weighted according to their income rather than their numbers. So there is a bit of merit to that argument, statistically speaking.
It's still a ridiculously high number, and when you factor in the impossible-to-factor costs like the depressing effect of regulation, and add inflation on top of that, it could very easily top 50%. I've seen some people claim as high as 7/8ths of our productiveness is sopped up by the government in some form or another. But you can't really get any hard numbers on that, it's all speculation.
The simple total-amount-of-taxes for the average person is currently around ~27-33%, so "a third" is accurate.