You are absolutely right to be concerned. That is why I am careful when selecting which YouTube video to include in my Hubs.
Many video on YouTube were uploaded illegally by people who are not familiar with copyright laws or who do not care. Just because YouTube provides you will an embed code for that video and the uploader has enabled the "share" feature for that video does not mean that you should include that video in your Hub.
For example, there are people who have recorded parts of a live concert and uploaded it on YouTube. Most likely, this has violated copyright. That is why many live events says "no videotaping". But people do it illegally anyways. So I do not include illegally uploaded videos.
Same with television shows. They recorded a snippet of television or movie streaming on their computer and they uploaded it. This is again likely an copyright infringement because the show producers never gave explicit permission for the person to distribute parts of the show on YouTube. So I never include videos such as those in my Hub.
The exception is that if the show producer were the ones who uploaded it. And the video is watermarked with the producer's logo so that clearly anyone watching it know that the clip is from the producer and uploaded by the producer. And if they turned on sharing. Then okay.
Now let's say there is a video showing a chef cooking a recipe. And it is apparant that the chef was the same person who uploaded the video to YouTube. And if the video has "sharing" setting enabled. Then it is reasonable to assume that the chef has recorded his/her cooking skills to demonstrate to the public and uploaded the video and allowed it to be share. All being the same chef. Therefore it is safe to include such video in Hubs.
I am not a lawyer. This is just opinion. I can be wrong.