The key here, I think, is that the method of delivery and payload has become more ambiguous over the years. Traditionally a virus requires human interaction to spread, whilst a worm requires no human interaction to spread. In the good ol' days, the "nefarious software" was highly specialized, meaning it was either a root-kit, trojan, or whatever it may be. These days, however, they've become wrapped up like a crappy Christmas present of coal (except worse), like, multi-purpose malware tools.
That said, I agree with you about not running two AVs at the same time (concurrently). This is because AV "A" will try to deal with the infected file, which in turn causes AV "B" to respond to "A", therefore causing "A" to respond to "B". The result of this is an infinite loop (i.e., "A" -> "B : A" -> "A : B : A" ...).