As long as you have the area code and the seven digit number, you should be able to locate any number's owner, if you know where to look. There are many many sites on the web that do offer free reverse phone look ups, but these only cater to landline phones.
The directories that promise you they are offering owner details for free are very likely making a misleading claim. Keep in mind that while they will give you the address, often apartment numbers may not be included in the listing, so if you will be sending something via snail mail to the person or business you are searching for, you'll want to make sure that you either know that they do not have an apartment or unit number, or that you have some other way of finding that out, such as by calling the phone number you find. Sadly, it appears that these numbers will be protected for a long time to come.
These websites naturally have to pay for access to some of this information, and go to the considerable trouble of pulling all the various resources together in one place. You can usually search for a cell phone number or you can get a membership. Most of the services charge you one time fees.
If you do not get results, you can get refunded by the reverse cell phone lookup service. If you rely on directory assistance and the white pages only, then yes you can garner privacy in that respect.