"She showed me the bank statement with the money coming in."

Coming in? Or, she Deposited it? Account Type matters; statements are for all sort of accounts and activities.

"They also did not withhold the customary 20%."

If it was Direct, they don't have to. If it was payable to her, it should have stated "IRA" in Payee name or FBO. FBO Jane Doe IRA.

"Either way, she missed the 60 day window. I may need to dig into whether the previous employer made an error that would get us an exception."

Well, now...She Spent the money. I think the employer is out of the picture, now.

Here's where I still find it confusing. You stated:

"opted to rollover her IRA,"

That's event #1.

"took the IRA distribution in the form of a check made out to her"

That's event #2.

If the employer sent the funds to the IRA account (401(k) rollover) and then she took a distribution from her IRA account (check in hand), sure, she took the action that now is taxable + penalty.

If, however, you described it wrongly and there is 1 event, then it is moot. She spent the money; you pay the taxes and the penalty. You hopefully had some fun.