This claim was raised again by the Charedi MK's today regarding the plan to give extra money to northern schools.
The government is giving money to all the public schools in the North. Charedi schools even if they get money from the government are not official public schools and therefore are not getting money. This claim is really a case of the Charedi schools wanting to have their cake and eat it too. On one hand, they won't let the government have any hand in what the curriculum is, what is learned, standards, etc. on the other hand they want the same money from the government as the public schools where the government has full control.
What is even funnier is that one of the things the government is giving is computers. What exactly are Chinuch Atzmai schools going to do with computers anyway?