Can general soap kill bacteria?
Soap kills nearly all the bacteria it comes into contact with by dissolving the bacterial membrane.  Some viruses with protein coats can resist soap, but many viruses have similar membranous coats (like HIV) and are usually disrupted by soap.  I'm sure it washes some away too, but to say they don't kill bacteria is misleading. In the end, though, they are gone. 

Antibacterial soap with triclosan does not kill bacteria on contact and are no more effective than if they had no triclosan at all.  That's actually a good thing since really using an antibiotic would probably accelerate antibiotic resistant bacteria which is a serious - probably catastrophic public health failure. A recent study showed that killing bacteria by soaking with triclosan took 9 hours to start showing an effect.

To achieve full sterility, surgeons bathe their gloves in iodine (see details in the comments below) and their instruments will be sterilized by heating them beyond the boiling point in an autoclave under pressure.   That's useful when you are breaching the skin in surgery, but the skin needs some bacteria to be healthy long term and works well to fend off bacterial infections.  

Your confusion seems to come from finding a page full of errors. Alice didn't really do her homework.