Pandu was actually quoting manusmriti.
159. The legitimate son of the body, the son begotten on a wife, the son adopted, the son made, the son secretly born, and the son cast off, (are) the six heirs and kinsmen.
160. The son of an unmarried damsel, the son received with the wife, the son bought, the son begotten on a re-married woman, the son self-given, and the son of a Sudra female, (are) the six (who are) not heirs, (but) kinsmen.
https://www.sacred-texts.com/hin/manu/manu09.htm
Karna was a kanina son of Kunti but he wasn't a Pandava. Moreover, since Kunti gave him up, she lost her rights over him the moment Adhiratha adopted him. Scriptures gave greater importance to the one who reared children.
If Karna's claim to the throne had substance, then even Vyasa could be deemed an heir to Shantanu.
"Bhishma said, 'When a person takes up and rears a son that has been cast off on the road by his father and mother, and when the person thus taking and rearing him fails to find out his parents after search, he becomes the father of such a son and the latter becomes what is called his made son. Not having anybody to own him, he becomes owned by him who brings him up. Such a son, again, comes to be regarded as belonging to that order to which his owner or rearer belongs.'
The Mahabharata
Book 13: Anusasana Parva
Kisari Mohan Ganguli, tr.
[1883-1896]
SECTION XLIX
Edited by Wistfulness - 5 years ago