It depends what the speaker is setting out to do. If their lecture is to people who have a background in the subject and who have enough knowledge of it beforehand to understand the jargon and follow the train of thought from one point to another, then more than half the work of understanding can be done by the audience and the speaker doesn't need very good communication skills.
If it is a talk to a general audience containing a few people with previous knowledge, and a lot with only a smattering, then it has to be carefully constructed so as to explain key basic points as they occur, to move smoothly from the simple and obvious to more complex points, and to avoid specialised jargon. It sounds as though the lady on "The Big Questions" was more used to addressing an audience familiar with the subject - or perhaps not used to addressing an audience at all.