Similarly, it would seem that Burke's team would be opening itself up to a really disastrous result by bringing the suit, because CBS would be able to depose Burke and potentially other people who would not normally have to give testimony. For them to bring the case, assuming they see it all the way through, makes their statements more believable to me.
The ransom note is one element, and I don't place a huge weight on it by itself. You still have the foreign, male blood DNA evidence that the Boulder DA said was found on three different sites (and two articles of clothing, presumably underwear). I'm sure Burke and just about every other family member and friend was tested and excluded as a match from that DNA profile.