For people having trouble with Youtube links it is due to the link containing an additional ''s'' . For eg if the link is https://****.com make it http:// and the video will show up properly.
Sounds like a firewall problem HTTPS protocol might be blocked from Lan to Wan wherever the website is hosted . thats a good guess id say. Its understandable as to why HTTPS would be blocked if someones hosting a web farm.
Could be something else. I did notice this problem too however.