Are TED presentations academically credible?
I think you are asking two slightly different questions at the same time:
“Are TED speakers and their ideas credible? (as in "likely to be correct")” I'd say yes, since TED's process for inviting speakers is at least as strict as that of many scientific publications. Most TED speakers are invited to speak at TED because they've become renowned scientists through their peer-reviewed publications.
“Are TED talks scientific (as in "usable to base your own science on")?” Here the answer is definitely "no", for the reasons you mentioned: they lack the information needed to be independently verifiable.
Note that this does not mean that their content is wrong or unscientific; it just means that the talks are incomplete from a scientific point of view, and thus not by themselves verifiable. But most TED presenters will previously have published the findings they present at TED in a regular peer-review scientific publication in a scientific format.
The bottom line is: you should treat TED talks like you should treat Wikipedia: use it to quickly understand new and interesting concepts. But before you actually apply one of these concepts, verify them using scientific literature.
TED talks are for popularizing ideas in science, technology and arts, as emphasized in their tagline:
Ideas worth spreading.
Very often they are a nice starting point to get interested into a certain idea and they serve as a general food for thought.
However, don't treat them as revelations, since:
- they are not comprehensive (in 5-20 min you can't give a comprehensive introduction to anything (some things require hours to explain, others - years of studies); moreover, if a talk is for the popular audience (as in case for TED talks), many crucial details need to be simplified or dropped),
- it is not rare that the presented idea is not considered mainstream (they do value originality; sometimes minority ideas can turn out to be a gold seam, which needs audience, in other cases it may turn out to be incorrect or inconclusive).
So, if you want to use the content of TED talks for anything beyond discussions over a beer, do consult other sources (e.g. scientific papers by the authors and check if the they are recognized in their field).
Also, very often checking out a relevant Wikipedia page gives insight into the status of a given view (is it present at all? is it disputed? is it this year's discovery or does it date back to ancient times?).
Or, as you did, asking experts (sure, they can be wrong too, but at least can be more objective than in a 15 min pitch).
Not exactly an answer to the question, but I'd just like to correct a factual error in the question.
The speaker doesn't give us his sources, therefore the talk is no longer be a scientific talk.
The time limit on TED talk probably prevents the speakers from disclosing all sources. I cannot speak for all of them, but at least for Hans Rosling (the one featured in your question), all the data source he uses are listed here.
he said that these statistics are unverifiable
This, I agree. Even sources are disclosed, we may not know if the sampling is well designed and executed, or if the measurement techniques are the most accurate. Some more exploration on our own in the data providers' site is perhaps necessary.
And the real scientists are clever enough to stay away these bullshit presentations.
To be honest, I feel that your anthropologist seems no better. It takes only a few clicks to verify the data source, and yet instead of doing that, he/she decided to call the talk "bullshit." I'd recommend you to be more careful about what he/she has to say on all other "scientific matters." Better to verify them yourself.