Id ask for justification of the extra money they asked for and ask them exactly that question, why will your server be seperate from the rest? its not like your doing anything that requires your own dedicated line.
Leaseweb have told you that it should be fine, but your very right to be cautious, have a look at their terms and conditions (TOS/Terms of Service) and see if it mentions anything about copyrighted media.
Its great your being cautious though as many people have put themselves in your position and ended up having their accounts cancelled due to that same exact reason - having copyright multimedia files on the account.
Best of Luck Dumpster!