I had a sub cover my classes for a few weeks a couple of summers ago. He was a student at NCKU. A competing school ratted us out and a woman from the Foreign Affairs/ Labor Affairs showed up at our school. She was threatening to have the teacher arrested and deported immediately. The school was also being threatened with a $2 million fine. Luckily, it was some how smoothed over and he didn't get kicked out and lose his scholarship. He was warned though that if he was caught again, he would be gone.

So it is definitely not a rumor. All it takes is one phone call from some idiot to cause the school and the student some major problems.

earning 'extra money' on a student visa is very much illegal.

The working on a student visa is a big gray area. The last time I spoke to immigration they said students can work to subsidize their living expenses in Taiwan up to 16 hours a week. The jobs that they can work are supposed to be basic jobs or unskilled labor jobs. Teashops, restaurants, bars, etc.

However as wages at most jobs in Taiwan are about 1/6th that of teaching English as cram schools. Most students prefer to teach. The gray area of this part is that schools can hire students as general employees, assistants, helpers, etc. But not as actual teachers. Being a teacher in Taiwan requires you to have a special ARC. Although most students that work at cram schools are teaching classes, this is technically illegal.

People have been kicked out before, people have lost scholarships, and on top doing this you will also have to pay a fine. 3-500 000NT. If you don't pay, you will also loose all credits. as National schools are connected to the Government.

Teach a few private classes, good luck if you take the chance of teaching illegally.

Get hip to the fact that there are, really, no rules in Taiwan. They exist on paper, but if you have the guanxi and the connections, everything is OK. If you don't, you will be raked over the coals for any minor infraction.

As a student you can work part time.
The problem is you have to get a letter from the place you are studying saying that they allow you to work part time.

NCKU won't give you one as their stance is your here to study not to work and you should have come with enough money in the first place.
Without.... and you are working illegally.
On that point any demos or sub work is illegal as the place you are working at do not have a work permit allowing you to work there.

I knew a guy that was teaching illegally at a school when the government "checked up" on the school and caught him. he ended up escaping through a bathroom window but lost his shoe in the process, so he had to walk home missing a shoe. 

Even working at a school outside of your ARC is worthy of being deported, so be careful.  They made it easier to add schools to your ARC about 5 or 6 years ago.  Just need to have that work permit.