I don’t know for sure so this is not an official answer, but my assumption is if youtube gives the embed code then the user must be OK with people embedding. To me that's sort of implied consent. When you grab the embed code it automatically links back to the source on youtube.
However I only use related videos and for the right reasons so I don't have any concerns about it. I'm sure they have help files that talk about all the legalities so you really should check there and not take advice from anyone on a forum, especially me!
I also suspect that taking someone else's work for your own gain and editing to put your url all over it is a copyright violation or could cause problems. Think about if you took hours to make a video and a bunch of people took it and used it to drive traffic to their own sites.