No it doesn't. The person was trying to say SpaceX > NASA. Many people here are trying to shit on the other side as if they have a real point.
They're both doing cool and useful things and they're both really really good at what they do.
I don't think it makes sense to talk about which is better unless there is some specific metric that can be measured so a conclusion could be reached. I am encouraged though that SpaceX has a trajectory that will allow greater access to space. By bringing the cost of space travel down, I expect we will get a lot more of it. NASA (and other governmental space programs) started the initiative, but I think SpaceX is continuing it marvelously.
Here's a breakdown: https://youtu.be/4TxkE_oYrjU
I watched the first 90 seconds of this. On the cost of re-usability of a falcon 9 point, the figures are shown as from Wikipedia.
So 1) not a primary source. 2) fails to calculate the percentage correctly between $62m and $50m as "around 10%". It's almost 20% on those figures. 3) and most importantly, those numbers are the cost to the customer, not SpaceX's internal cost. As they have no current competition in rocket re-usability, they are able to recoup the R&D cost for developing this technology.
I don't think I'll bother watching the rest of the video.