There's no full-proof way to prevent people from recording video and sharing it, (can always just take a video of their screen if it comes down to it) but depending on how much effort you want to put in you can make it a lot more difficult. The Adobe Media Server has some features that allow you to prevent recording streams and only letting authorized people view them.
Have used the strobe media playback framework for self hosted videos a lot which at least prevents people from sharing the youtube links and searching your videos, and they would probably only be able to access the links from within your survey. There are some other similar projects too for hosting your own videos. (JW Player comes to mind) These also give you more options than an embedded youtube when integrating them in your survey. Can for instance set it to not allow you to continue until the video completed event is triggered.
As quick and dirty method to embed a video without youtube, upload the video file (.flv or .mp4 works) to your server and enter the url here: www.osmf.org/configurator/fmp/