What they (TSP) takes out of the withdrawal and what (comes out of the wash) at tax time are two different things. Furthermore, any state taxes on the withdrawal takes place only at tax time.
I took out a TSP hardship withdrawal while waiting for my Federal Disability Retirement. If I remember correctly, I withdraw about $35,000. TSP took no more than $5,000 of it in taxes. At tax time I paid a lot in state taxes, and some on the TSP and the back pay to the IRS; but, it was no where close to 20% or 30%.