The entry/non-entry of Dr. King's speech into the public domain is a famous case in copyright circles - and in fact, was one reason the copyright laws were changed. It's a fascinating story.
First you need to realize that prior to 1976, unless you put a copyright mark on a document and properly registed it, it was presumed to be in the public domain as soon as it was made public. This led to a number of problems and disputes, and today is widely viewed as being overly punative to people who simply forget to put the mark on a document before releasing it. Today's copyright laws eliminate the "all or nothing" nature of the 1909 Act, and sensibly declare that copyright rests with the author, regardless of whether they properly marked it.
Second, there's an interesting history behind the I Have a Dream speech. While the factual accounts of exactly what happened differ, Dr. King and his associates apparently distributed advance copies of the speech without the copyright mark on them to a group of journalists. Recognizing that this was a serious error, others within Dr. King's circle reportedly re-collected each of the advance copies, and then redistributed them with the copyright mark hand written on the document. So there was a factual question as to whether the textual copy of the speech was put into the public domain or not registered with the copyright office correctly.
There was less dispute over the video and audio. As others have noted, Dr. King improvised/departed from the prepared text a number of times. So there was an argument that, even if Dr. King had lost the copyright on the original text (which is itself debatable), he maintained the copyright on the "performance" of the speach, and was thus entitled to a separate copyright (see http://en.wikipedia.org/wiki/Estate_of_Martin_Luther_King,_Jr.,_Inc._v._CBS,_Inc.).
I also believe that the speech is freely licensed to anyone engaging in educational activities - so it's not quite as eggregious on the part of the family as many have suggested.