I think this type of advertisement(if not a public school) is indecent, especially using those words in the title. It is misleading to potential employees, could potentially waste their time, or even cost them a really good opportunity.It is like the University jobs(some not) posted on ESL sites.
Be aware of ads titled "Public school teaching!
I know what you mean. Some of these agencies are wasting your time. They may be posting public school jobs that don't exist, in order to get you to work in a dodgy hagwon, or worse. I had a recurrent problem with certain recruiters in China who advertised non-existent jobs. There was also a recruiter on Seoul Craigslist who advertised okay jobs in Seoul, quoted Corinthians and offered me a completely different kind of job on a mountain somewhere. You can apply to some hagwons directly. Applying directly to EPIK is also an option.