Well, to be fair, Durham have a slightly confusing two-tiered approach to contextual applications. This is explained (poorly) in the Contextual Admissions section of
this page on their web site.
Essentially, then are a series of
contextual flags which can be associated with your application (e.g. "the school’s or college’s performance is below the national average" or "a student is known to have been eligible for Free School Meals (FSM) in the previous six years"). Any of these gain you "additional consideration". They
may use that information to:
"- to make an applicant a standard offer where the applicant’s academic record (eg, GCSEs/AS levels or equivalent) or personal statement may be marginally less competitive than the cohort overall
- to make an applicant a standard offer where the applicant is predicted marginally below the usual entry requirements
- when making confirmation decisions for offer holders that have marginally failed to meet the entry criteria (usually this means one grade below the standard entry requirements)."
The above is perhaps where you got your "had to hit that AAA entry requirement" from, as the above does
not include a grade reduction at the offer stage.
Then, separately, they have
contextual offers - which come with a reduced grade requirement. This is available to "students flagged with a home postcode that is classified as POLAR4 Quintile 1 or IMD Quintile 1, as a care leaver, or a participant in a specified LSE WP programme or a Sutton Trust Pathways programme". (Even then, that say such students
may be considered for a contextual offer - so they've left themselves some wiggle room.)
So contextual offers are available to a subset of students who have contextual flags.
You've said "I should be eligible for a contextual offer", which presumably means you feel you fit into the second category. Such candidates will have a lower target to hit, in terms of the entry requirement.