Not necessarily. That would be true if the absolute $$$ collected were the same, but that's not what is asserted.
Consider the following: 10 people earn $10 and pay $1 in tax. 10 people earn $20 and pay $5 tax.
The total tax collected is 20% of all income.
Suppose the government raises tax rates such that the $20 earners will now pay $8 tax.
Say 4 of the high earners stop working as much (since their marginal rates are so high).
Now you've got: 14 people earn $10 and pay $1. 6 people earn $20 and pay $8 tax.
The government now collects 24% of all income. It also collects a higher proportion from the lower income people than it did before. It has lower revenues and people are, on average, poorer. In other words, everyone loses.
So you can't just look at effective tax rates to determine whether raising top end tax brackets was good or not.