You have probate, but state there is no estate. But probate is used to settle what is in an estate and outside of a beneficiary arrangement. So, you have an estate?

This isn't really worded correctly: "If filed on 1040, spouse would have to pay the taxes on loan that she was not legally liable for to begin with."

The Loan was from that account, which makes it hers, now. Date of settlement makes it hers, as the account became hers, when the transfer to the beneficiary was settled, because of his death.

If this 1040 is on extension, there still is time to rollover the amount of the loan offset for tax management purposes: "Effective January 1, 2018, if the plan loan offset is due to plan termination or severance from employment, instead of the usual 60-day rollover period, you have until the due date, including extensions, for filing the Federal income tax return for the taxable year in which the offset occurs."

From: https://www.irs.gov/retirement-plans/retirement-plans-faqs-regarding-loans#2

Otherwise, the amount is considered to be a taxable distribution, which was settled to her.