Tax question for lawyers et.al

I was told recently that someone won a $500,000 law suit. It was appealed and the final settlement was reduced to about $325,000.
The person paid the lawyer about $125,000. They were told by two tax attorneys that they had to pay taxes on the original $500,000 award AND had to pay taxes themselves on the amount the lawyer got too.

I assume this must be right if two tax attorneys agree.
I assume that the lawyer will get taxed on the amount they received also.
First, isn't that double taxing the legal fees?
Second, why would they have to pay taxes on an amount they nere received?

Please inform the weak of legal and tax minded!

Thanks