What kind of JOIN are you trying to perform?

I do believe that when you do not specify the type of join it is "INNER JOIN" by default. So, try with a LEFT JOIN for example:

SELECT      DISTINCT p.person_nbr AS 'Person Number'
            ,CASE 
                WHEN MONTH(GETDATE()) > MONTH(date_of_birth) OR MONTH(GETDATE()) = MONTH(date_of_birth) AND DAY(GETDATE()) >= DAY(date_of_birth) THEN DATEDIFF(YEAR, date_of_birth, GETDATE())
                ELSE DATEDIFF(YEAR, date_of_birth, GETDATE()) - 1
            END AS 'Age'
            ,primarycare_prov_name AS 'Primary Care Provider'
            ,CONVERT(VARCHAR(20), CAST(datetime AS datetime), 101) AS 'Encounter Date'
            ,encounter_id AS 'Encounter ID'
            ,rendering_provider AS 'Rendering Provider'
            ,primary_insurance_name AS 'Payor'
FROM        ED_PHE_encounter epe

LEFT JOIN   person p 
ON          epe.person_nbr = p.person_nbr;

There are three reasons why a query returns zero rows:

• One or more tables are empty.
• A WHERE condition is filtering data out.
• An INNER JOIN is acting as a filtering condition.

Since you stated none of those two tables are empty, and you do not have any WHERE condition active, the only thing that comes into my mind is that the join fields do not match, therefore acting as an inner join the interception is the null subset. You might want to make sure that there is actually a match between epe.person_nbr and p.person_nbr. This check is easy to perform, simply left join the distinct key fields of one and the other, and see if they match.

Hope this was somehow helpful.