Previewing a view does not show a phone number but when I look at the view by visiting the URL of the page it does? I have taken over a Drupal website and I am completely new to Drupal. One of the features of the website is to list out all the employees of a company (a Directory). 

The directory is displayed with a tabled view, and is pretty easy to understand. 

When I look at the view while editing it in the preview view I don't see the each employees' list of phone numbers, I dont see a field for those numbers (i.e. Content:Phone_Number) either, but when I actually look at the view, from visiting the URL of the page I see the phone numbers. 

Additionally, when I visit the URL that is hosting the View and use Firebug (DOM Explorer) I can see that there is a td tag that is holding the phone numbers. But, when I visit the View from a editor standpoint and check the preview view with FireBug (DOM Explorer) I see that exact td tag, but it's holding the user's NID number, not the phone numbers!

How is this possible?

Please and THANK YOU.
They most likely modified a tpl.php file.  In the Views module when you are viewing to edit it, look for Theme: information and click information.

You will then see a list of possible tpl.php files.  If you see one that is not in the first position and bold, then you know they did some type of override on the tpl.php.  Look in the theme folder for that file name.

If its not in there, then you will want to look at your themes template.php for some type of override.  Finally, some people will put these overrides in a utility module.