From the beginning, you state surviving spouse. But you never directly answered if this spouse was listed on the deed as an owner, owner with right of survivorship (and therefore inherited), or tenants in common. So, that's one choice of three that makes a difference, both for basis and for gain.

Example: If the spouse was joint owner, and with right of survivorship, then she owned 100% of the property after the date of death.

"The house was sold less than 2 years after the date of death, so the surviving spouse also qualifies for the entire 500K exclusion."

Yes, that's a Federal tax provision. That doesn't affect real estate ownership. That long after death, the house would have been owned by a person who was not dead. There is no estate for the sale of the house. The surviving spouse owned and sold the house. It should all be on her taxes and reported by her.

Whoever gave the guidance to the listing and the sale apparently did it wrong.