By etiquette you should always acknowledge other people's work in your posts and this goes for embedded youtube videos as well (e.g.: video by John Smith).
However you don't have to seek any kind of permission to embed someone else's youtube video into your posts.
Youtube specifically allows other sites to embed its videos (to maximize traffic/ad revenues) and Youtube content creators can disable embedding if they don't wish their videos to be embedded by others on various sites (that's why sometimes you see a video blacked-out with a message reading "Embedding disabled") or they could even Unlist a video so only they have the link to embed it on their own blogs.
Moreover the video technically always remains on Youtube and on the original youtube author's page, who will still be benefiting from increased views and monetization through Google Adsense.
As long as you don't claim the youtube video to be yours when it isn't, then you are not committing any abuse on Steemit.
I've noticed a lot of misconceptions and confusion on this. I hope this helps clear it up.