I received a new answer from the technical support, that clarify the situation a little bit.
The domain ab-cd.com is already configured on our servers, and we can't use it again, because of a DNS restrictions.
This answer, of course, make more sens then the first one. Now, it's a matter to understand how they did configure the things.
I will keep you posted, so at least someone can learn from this experience, once it will be solved.
/* Answer for this issue */
Finally, The mystery unfold. The site live version of ab-cd.com was host by iweb.com The developpement site of ab-cd.com was host by funio.com These 2 compagnies are the same, and use the same servers.
This information wasn't cleary communicate, creating the confusion on my side. And that's why, they wasn't able to configure the server with the correct address ab-cd.com, so I can use modified hosts files to preview my site, even if they was able to do it for any other address of my choice, even the one that was not my own.
Hope that will help someone who might find itself in a similar situation.
Thanks