Weird charge in insurance plan

I’ve been living in the Netherlands as a student since August, and the health insurance I had up to about a month ago was the European Health Insurance Card. However, at the end of December, I had to swap to a Dutch health insurance company, as obligated by Dutch law if you are about to start working. Some days ago I received a mail by the company where they state that on top of this month’s subscription I also have to pay for the period I’ve been living in the Netherlands (i.e. 5 months amount!), which sounds absurd since I was insured for that time. I called the company and they informed me that "that’s how the law works in the Netherlands"… Is it really this way?