Well if their IT department is anything like the Healthcare.gov initial team, or other government agencies. What I've heard from Code For America. This is totally realistic.
For those downvoting, see here: https://news.ycombinator.com/item?id=7891622
Maybe it's the time I've spent in corporate environments, but losing data due to shitty IT management seems very plausible to me.
If you told the IRS you couldn't file your reports because you'd lost user data they'd consider it criminal negligence, I imagine, that you'd not secured the data through backup. Sauce for the goose ...
Data loss where there's no backup system even in place sounds like reason to fire all the IT managers in systems like the IRS where the preservation/security of data is vital to proper function.