They're right....no real need to sanitize anything pre boil, as the boiling takes care of that for you. It should be thoroughly cleaned of any buildup, deposits, whatnot, to avoid any possible off flavors, etc. Basically you clean the stuff for the same reason you clean your cookware....but not necessarily sanitize it. Spray the goop off your immerison chiller, then immerse it into your boiling wort about 15 minutes before flameout to sanitize.
It's once you cool the wort below boil temp that you have to be careful....esp. once you get around room temp. Lots of nasties floating around looking for a meal, and that sweet liquid is just the place for them. So, sanitize anything that will come in contact with your wort (or beer), post boil.