Not that I don't believe you (the word 'necrotizing' sends shivers up my spine) but since you didn't catch the spider itself, are there any other species of spider that may have been the biter?
I take it your never been to Mt Diablo during mating season then? The place is filthy with tarantulas. Just a random YouTube but at certain times of the year, the road is covered in them: https://m.youtube.com/watch?v=g4w5UbvaYy0
My experience with BW bites was my dad getting bit a couple times growing up out in the Central Valley. He had bad flu like symptoms for a few days from the bites. FWIW
In Virginia there are only two known populations of venomous spiders, the black widow and the brown recluse. A black widow bite was ruled out because I did not exhibit any of the "typical" symptoms that they'd had experience with. I didn't have any pain outside of the bit marks (until later when my lymphatic system started to show signs of blood poisoning and an ache set in). From what I understand black widow bites start off as a "bee sting" type pain and then progress to abdominal pain and full-body muscle spasms.
But as you alluded to, without a specimen, it was an educated guess on their part based on my memory of where I'd been during the week prior to the bite.