Guess it was too difficult to just adjust the pay amount (with a deduction) for the next pay period?
The second problem is, they have to get all that money back. If a federal employee is accidentally overpaid, the government can only recoup 16.67% of the amount of the overpayment per paycheck pay period. You can’t take it all back at once. So then they had to write a special payroll job to pull all this money back. It took ‘em like four or five months to get it all, but finally it was all accounted for.
It suggests that even if technically and/or legally the option exists to recover the money directly from you, it's not part of the procedures that govern this type of thing (...as of today. It may have been in the past. Indeed, these procedures may well have been drawn up pursuant to the event discussed in TFA).
Even now, at my Federal government job when someone is overpaid we issue them a "debt letter" and then reduce their pay until the account is balanced. I assume it's because of the same reg/statute that fixes the clawback to 16.7%.