Grammar and punctuation; is it important for today's authors?

I saw something on this morning’s BBC news. Unfortunately I couldn’t hear it properly as I was in the bathroom brushing my teeth.

The author was arguing that it wasn’t that important and from what I heard, I agreed with him to a point. The person in opposition was arguing that grammar and punctuation were vital in order to be understood. Does this apply to writers today? I mean, if you write in the vernacular you are going to use your words as they are spoken. As we live in a technological age, is the written word as important as the spoken word? Would love to hear what other people think about this.