I can tell you from first hand experience, so long as you remain calm,
you can let them walk on your body without a problem. If you do something stupid to enrage them, they may well give a nasty bite and you may well suffer headaches, nausea, pain and swelling, but in general, you wouldn't require hospitalisation. Now, if you come across that other Aussie spider referred to in the abovementioned video, keep well away from it. Very nasty little buggers.
You are right, for the most part, the biggest problem can be serious infection, I have been bitten by 3 spiders in my time,
-Redback on the hand, I was in excruciating pain, had a red line climbing up the vein in my arm, Grandmother gabbed my hand, sliced it open with a razor blade, hot water then some kind of disinfectant........thats how they did it back then......it worked!
-White Tail Spider, painful, got dizzy but no other side effects
-A big red spider, bit me on the toe (40 years ago, sometimes I get pain shoot up that toe but goes away after a while)
Many years ago, I had an all expenses paid job in South Vietnam, one of the guys had a big interest in bird spiders, used to dig them up and walk around showing off with them on his arms/head etc
One day one them got sick of being wrangled, so slammed the fangs into his arm, looked like someone stabbed his arm with 2 pencils
With a stream of blood pouring out of both wounds, he said, " no worries, they are not venomous! " but was going to the doctor to get it cleaned up,
Went to the doctor, straight away, said, " I'm an expert on spiders, I know they are not venomous, just clean it up for me! "
Doctor said " you are right, they are not venomous, but in this location..........they carry Rabies! "
This guy was very quiet for the rest of the tour, and never played with spiders again
His biggest problem then was the very long and painful treatment for Rabies
Sorry for the long story, thought it may be both educational and amusing