I think the "back up" we are talking about is redundancy. For example, your ropeman or whatevever shouldn't slip, but if it did it could slide off the rope; however, if you tie a stopper not on the end then you are "backing up" your system or mitigating risk by making the rope more than 1 fault tolerant. Now your ropeman would have to fail (1 fault) then your stopper knot would have to fail (1 fault) = 2 fault tolerant instead of 1. What you decide to "back up" or be redundant on will vary from person to person.
2nd example: I can rappel on a figure 8 or my carabiner all day long just holding the rope in my hands; but, if I lose grip I will fall (1 fault tolerant). If i add a friction hitch like a auto block or french prussic to my rope I add redundancy to my system such that if my hand slips the friction hitch would catch it. No one is saying wrap yourself in bubble wrap, but I do think Bill is trying to encourage people to consider mitigating risk of falling or getting hurt by backing up your system where you can.
Last example: Some people feel safer with 2 tethers. In the off chance that you cut your tether line somehow, you would fall, but would be caught by your second tether. Do I think there is a high likelyhood that I'll cut or that my tether will fail, no. So that is a risk that I scale as low for me and therefore decide not to back up. Other people might assess that higher and want to add redundancy to that part of their system. I don't want to ever fault someone for adding safety mitigation to their system. I think it is only fair to fault someone for being unsafe and encouraging others to be unsafe.