I think there's some semantic confusion here between the bad software (adware) and the software that removes it (Ad-Aware and Spybot). Adware is software that installs pop-up ads on your machine; it's what the links are referring to.
Ad-Aware is a program by Lavasoft that removes adware; so is
Spybot Search & Destroy. I usually recommend using both since they tend to catch different things. I am not aware of either of these programs causing problems with PCs.
Nanny software is often used to block certain sites from surfing. Usually in households that have children. If you haven't installed nanny software, then you don't have any