When investigating I found out that the problem only happened with
YouTube movies that were embedded in an Iframe.
The problem did not occur with Vimeo movies that were also embedded
using an Iframe.
Since there was no difference in the Iframe embed code, the only
possible difference was the Youtube vs Vimeo link.
I found out that in an iFrame, the default wmode is windowed which
essentially gives it a z-index greater then everything else and it
will therefore overlay over anything.
By appending this the wmode=transparent parameter to the Youtube link,
the Youtube Iframe wmode is transparent and will therefore stay behind
the Slimbox overlay:
<iframe src="
http://www.youtube.com/embed/b-LJ7pYNI0I?
wmode=transparent" width="590" height="332" frameborder="0" ></iframe>
And this did the trick for me!