The exchanges don't collect taxes. Tax office probably requested information from the exchange and the exchange complied, and the tax office calculated the total amount withdrawn as taxable. The idea that an exchange would be calculating taxes is ridiculous.

If a sale is reported to the IRS and the exchange doesn't know (or doesn't report) the cost basis of the coins then the person who sold the Bitcoin is responsible for reporting their cost basis. If they didn't report a cost basis then the IRS is going to come back and assume it's zero.

He did the filing with the tax form that company sent. I think the exchange he transferred from was sketchy or not confirmed. In that case, when you sell, they show the full price.

I mean even if the exchange messed up and took out more tax than they should have, he would just fix that at tax filing time and get a refund.

If the exchange was overseas/super sketchy it's possible that the exchange just plain stole some of his money and claimed it was "for taxes."