Is there a noun for "someone who has access"?

possibly the word you are looking for is permission or privileges:

One could have permission to the data

or

One could have data access privileges

permission: consent; authorization.

privilege: a special right, advantage, or immunity granted or available only to a particular person or group of people.

source: http://www.dictionary.com/

'Privileged User' seems to be what the software security companies are calling them :

Top 10 Ways to Identify and Detect Privileged Users

Stealthbits

In law, specifically in premises liability, there is a set of words describing various levels of authorization a person might have to enter upon land of another: trespasser, licensee, and invitee. Putting it simply, a trespasser enters without permission of the other, a licensee enters with permission of the other but to benefit himself, and an invitee enters with permission but to benefit the other. I am a licensee when you invite me to come onto your land/house for a social event. (I am your guest.) But I am an invitee when I go into the Apple Store, because Apple has granted me permission impliedly, and because Apple stands to benefit financially from my presence in its Apple Store.

You could analogize and call the "internal data accessor" an invitee or create a neologism, such as admittee.