You can bet that the Royal Family has already taken the "maybe" out of it. Sometime along the line, in some pediatric doctor visit, his blood has been tested and they know the truth. There's simply no point in making it public or an issue since Harry has virtually no chance of getting anywhere near the throne.
...and Diana is certainly not around to stir the pot any longer.
And I didn't like her from the get-go; she was ALWAYS a most unsuitable choice, for Charles, who only grew worse as time went on!
OTOH...she was better than SPARKLES...which is saying quite a lot!