Acid free vs. "regular" matting for framed art.

My oldest son is quite the artist. He has a couple of pieces that have been needing frames for awhile. A local craft store was having a 50% off sale on frames so I (finally) picked up a couple. I also had some mats cut from material that they had in stock. I framed the pictures and they look great.

I was back in the store today to pick up some other supplies and noticed that the matting material I chose previously was not acid free. My question is: how much does this really matter when it comes to matting material?

The mat really only contacts the artwork along a very narrow strip around the borders. Is it possible for the acid in the mat material to leach further into the artwork or would any potential aging be limited only to the points of direct contact?