It looks like this is a problem concerning Safari's Flash sandbox. I have the same problem on a Mavericks app I'm developing at the moment. I added html5=1
to the video arguments list, effectively forcing HTML5 video.
Yours in that case would be:
NSString *html = @"<center><iframe width=\"748\" height=\"461\" src=\"http://www.youtube.com/embed/SV1cVDhKZ6g?rel=0&html5=1\" frameborder=\"0\" allowfullscreen></iframe></center>";
If you definitely need Flash, I haven't been able to find a more elegant solution.