RIP tomatoes

It's been less than a month since I diagnosed my tomatoes with fusarium wilt. In that time they've continued to ripen, I've gotten about two dozen rouge de marmandes (minus a few more with blossom end rot) and several cereal bowls worth of Tommy Toes.  But the plants went from this on January 17th:

To this on February 6th:

The poor things hung on for a while but once they started downhill they went down fast.  On Wednesday I picked another set of ripening Tommy Toes but the seeds inside were black.  That's when I decided they had to go, despite a few more fruit desperately clinging on.

But when I went to complete my diagnosis I was in for a surprise.  This is what the inside of the stem looked like:

Those white bits are perfectly healthy tissue.  With fusarium wilt they're meant to be discoloured brown, like this.  So now I'm confused and frustrated.  Did they really have wilt?  Should I have pulled up the plants or left them longer?  If it wasn't wilt what else could have made them cark it so quickly?  And how do I keep this from happening next year?