Thru the goverment , no , only if you can prove you didnt want the penalty by suing your employer,
your likely not to see the penalty , sorry.

You absolutely should get your money back since at the age of 62 you are entitled to all your 401 K money without penalty, although by taking it directly in a lump sum as you indicated, you will have to pay taxes on it. Contact the head of the HR department in writing, certified mail, with a copy to the CEO and explain the error and the dollar amount. I don't know of any provisions where a company can claim charging you 10 % is tax withholding, it isn't, it's a penalty and it's your money.

Give them a time table of thirty days to respond as to what they are doing to rectify the situation and ask for documentation of any correspondence with the plan trustee and/or the IRS. I wouldn't threaten them with legal action, just make it sound as if you innocently gathering ammunition for the pain and suffering this is causing you in your "golden years."

At the worst, you'll get it when you file taxes for the year of the withdrawal, because the "penalty" will be part of your federal withholding. If you don't owe it, you get it back.

If you checked the box before you signed the form, your goof, not theirs. Some senior citizens have enough other income that they actually want as much as possible to be withheld from their retirement distributions. Not up to the plan administrators to figure out if that applies to you or not.