What you’re not getting is that the taxes they took out are not permanent: you can get them back if you do the rollover for the original amount. If you don’t, then you’ll owe taxes on the part that’s missing - ie, the amount they took out to withhold. The amount you’ll owe is less than what they withheld, so you’ll still get some back, but not all.

If the original total was 1000, and they withheld 200, and you deposit 1000 into an IRA or 401k, then you’ll get 200 back from your regular tax return next year.

If you deposit 800 into an IRA or 401k, then you’ll owe (200*30%) or thereabouts, so $60, and get back 140 in your tax return next year. But that’s $60 less than you would otherwise get back.