Brown recluses are indeed a menace - have seen them in my home. One does not die or lose limbs from their bites though. They may if they do not treat the infection that comes from necrosis that the venom causes.
I used to work with a guy who had gotten bitten by a brown recluse on his thumb.
Doctors tried all sorts of treatments, finally got to the point of “If this one doesn’t work, we’re going to have to amputate your thumb”.
Fortunately, that last treatment worked.