My server administrator told me it was not possible to have OTRS and WHM/CPANEL on the same server. Is that correct?

I think people were able to use it on a cPanel server. I would suggest to do a search for OTRS here and also at cPanel forums.

I searched already both here on wht and cpanel forums. Only information I could find was way back from like 2005-2006 for an out of date version of Otrs