I'm all for biofuels. Global warming or no global warming, petroleum is a finite resource. Burning it makes no sense if we can burn something else instead. But the spiel in the video about how this is a positive thing with regard to global warming is simply nonsense. Biojet emissions are no cleaner than Jet-A- emissions.
If the question is how much CO2 is emitted into the atmosphere over the course of the flight itself, you are of course right. CO2 emissions for biojet vs. petroleum jet fuel are within a few percentage points of one another.
But, you are missing a big part of the picture. Making biofuels either involves growing biological matter as a crop to turn into fuel or capturing waste biological matter (like the tree bark use for the fuel in the article). Growing a crop takes CO2 out of the atmosphere (which is then returned to the atmosphere when the fuel is burned). As for the waste matter, if you just let it rot (in the field or in a landfill), the carbon content in the waste ultimately ends up as CO2 in the atmosphere (or perhaps methane, which is worse).
So, by making the biofuel, you either take CO2 out of the atmosphere to grow a crop, or you prevent CO2 emissions that would have resulted from rotting. Either way, the production process reduces the amount of CO2 in the atmosphere. Of course, that benefit is reversed when the fuel is burned, but at least in principal you could have the two balance out and be "carbon neutral."
For example, the hippy lady down the hill actually believes that she's doing the earth a favor by burning wood rather than propane. She raves on about how wood is "carbon-neutral" because the carbon was taken out of the earth and sequestrated in trees a hundred or so years ago. But the same can be said of any carbon-based fuel, when you get right down to it. And regardless of how or when it was sequestrated, when you burn it, the carbon is released now.
The carbon in your hippy neighbor's wood is going to end up released to the atmosphere someday anyway, when it dies and rots. If she cuts down a living tree to burn, she is just speeding up the day that happens. But, if a new tree grows in its place, then that carbon will be recaptured into that new tree.
If she burns propane instead, and that propane came from natural gas in geological formations, that is a net increase in CO2 in the atmosphere, because there is no process to return atmospheric carbon into geological formations on any reasonable timescale. (This might change if carbon sequestration technology were implemented on a large scale, but it's not clear that is feasible.)
At the end of the day, the carbon on this planet exists in (1) gases (mostly CO2) in the atmosphere and dissolved in the oceans, (2) living matter, (3) fossil fuels, and (4) carbonate rocks. Increasing the amount of carbon in #3 and #4 happens only very, very slowly. So, removing carbon from #3 inevitably increases the carbon in #1 for a long time. By contrast, carbon removed from #2 can quickly be replaced--indeed life will largely take care of that by itself without our help. Assuming biofuel production is done responsibly, it isn't going to really change the average total amount of carbon in #2. Since the amount of carbon is fixed, and you aren't touching #3 or #4, use of biofuels doesn't really change #1 much either.