I agree with you.  Although this link doesn't directly state that for a situation of 'electing' to only take part of the payment, I think it does show the concept that the tax deduction is for what the insurance won't cover.
https://www.irs.gov/publications/p547#en_US_2018_publink1000225265

As a side note, what does "opted not to itemize and take the 80%" mean?  To me, that means that $431,900 is not a proven amount, and if it was a proven amount, WHY ON EARTH would the taxpayer choose to not take $86,380 just to save some paperwork?  That seems REALLY fishy to me, and likely means the REAL amount is closer to the $350,000 mark.