As the DWP hold the purse strings, they have every opportunity to get any overpaid monies back.
I would expect some explanation of how the overpayment was miscalculated and for how long it's been paid. If it's been going on for years and recovery of the entire overpayment will cause hardship, I don't think there's a realistic prospect that they'll be able to recover it all.
Equally, as you say, the sum mentioned in the letter could be a mistake. Either way, it's upsetting for your daughter until it's resolved and not something you'd expect to be hit with out of the blue via a letter in the post.
A phone call from someone at the benefits office to clarify things with your daughter would have been a better first approach considering the potential sum involved I'd have thought.
I hope she gets it resolved soon and doesn't have sleepless nights.