The Joongang Daily has more information on this, and makes it sound like the teachers described in the KBS report were all among the 33 arrested. Or not. It's hard to tell for sure.
From a Yonhap report today:
42 people booked for illegally placing native speaking instructors in elementary and middle schools
(Suwon - Yonhap News) On August 29 the international crimes division of the Gyeonggi Police booked without detention six people, including recruiting company president Ms. Jeong (44), for illegally introducing native speaking instructors recruited from overseas to domestic educational institutions, in violation of the Employment Stability Act.So, to clarify, 6 people were busted for running a recruiting business illegally, but the 1,400 (!) teachers they recruited were otherwise qualified for their jobs. That they were able to operate for so long and recruit so many teachers suggests someone on the government side was lining their pockets. In the other case, 3 people were busted for connecting 'foreigners living in Korea' (33 of whom were busted) with Koreans wanting private lessons, and it sounds like the recruiters were both setting the fees and collecting a portion of them.
Police also booked without detention 33 unqualified native speaking instructors as well as three recruiters, including internet cafe operator Mr. Lee (31), for introducing unqualified native speaking instructors to private customers.
Ms. Jeong and the five others are charged with operating employment agencies, which were not registered domestically, in places like the US, UK and Canada since 2011 and illegally introducing around 1,400 native speaking instructors they had recruited to the National Institute for International Education as well as city and provincial education offices.
It was revealed that the referral fees for each teacher were around 800,000 to one million won, which adds up to 240 to 350 million won in fees that they received.
The native speaking teachers that Ms. Jeong introduced worked as assistant teachers in elementary and middle schools throughout the country, in places like Seoul, Gyeonggi-do, Incheon and Ulsan. Police said that through they found a job through an unqualified job placement company, the foreigners had instructor qualifications.
Mr. Lee and the two others have been charged with running a native speaking English instructor recruiting website from January to July this year and collecting placement fees for introducing foreigners living in Korea to private customers.
Introducing instructors who made 60,000 won per hour and charging a placement fee of 20,000 won for each instructor, they earned around 70 million won.
As to whether the foreigners they hired were on E-2 or tourist visas, there are definitely theories out there. This bust appears to have been mentioned in a KBS report from August 23 about arrests of unqualified foreign instructors and the hagwons and kindergartens that hired them. The report begins with a foreigner teaching English at a Taekwondo academy who says he is on a tourist visa, and then lists the results of a month-long crackdown by Suwon immigration office: 13 unqualified foreigners who were working as English instructors at 7 places - kindergartens or art, music or P.E. hagwons. One kindergarten had hired a Russian and an Uzbek to teach English, though an official there said they had no idea the teachers were on student visas (of course!).
The report also says a broker who recruited around 20 foreigners to do illegal private lessons was also caught; this may be related to the bust announced today.
It's then explained that native speaking instructors need E-2 visas, which require effort to get, while hiring unqualified people requires no such effort.
The report then ends by saying:
An average of 1,000,000 foreign tourists come to Korea every month. Among them a good many earn money as native speaking instructors, but only 140 were caught in the crackdown nationwide."
I doubt anyone has any idea how many people on tourist visas teach English, but it's certainly a small percentage of the million foreign tourists who come every month, not 'a good many'; luckily, that term is vague enough that it can be used. The more interesting thing to note is the 140 who were arrested. This isn't mentioned anywhere else that I can see, however.