Aren't they talking about sodium metabisulfite here rather than sodium percarbonate?
Must be. There is no sulphur at all in sodium percarbonate. It breaks down in hot water to form oxygen gas and sodium carbonate The process produces a highly effective cleaning agent - whilst it is fizzy - and once the oxygen has been released then the residue is pretty harmless. Sodium carbonate is also known as washing soda. It is non-toxic, mildly alkaline, very soluble in water and therefore easily rinsed off to leave a clean surface. It definitely does need rinsing, though.
However, the HBS advice is good in as much as it is a cleaner. It is not a steriliser.
To sterilise, you need to use something labelled as such - or bleach as you suggest.
Personally, I use lots of thin bleach. But, I never dilute it. I use it full-strength on previously cleaned surfaces, let it do its job for maybe 10-20mins, and then rinse thoroughly. Why dilute it? All you're achieving is to dilute its sterilising power.
My protocol is:
Clean first (you cannot sterilise a dirty object)
Then sterilise (OK, it won't be lab-standard sterile, but for homebrewing purposes it should be fine)
Then sanitise after rinsing (Especially if, like me, you're on a private water supply which will be far from sterile. Good practice anyway to keep things sanitised to avoid any "nasties" starting to colonise)