That is true, but only on his deathbed ánd after Alicia and Alexia have been discreet all these years. I have the feeling that Prince Bernhard would have been equally stubborn als Albert, had Alexia run to the media:
"Wait a minute... I bought an arch expensive penthouse at the Avenue Raphaël in Paris, I sponsored her and now she bits me in the hand? No way!" I can almost film it, Prince Bernhard's reaction. I feel the Prince has acknowledged them as daughters because they played the game and followed the rules.
He told her to leave him alone about this and that he's not her father as soon as the rumors came out. She was discreet before then. If he was willing to work behind the scenes and help her mother deal with that situation, I wonder what would've happened?
She knew for 12 years by 1999, and she was discreet before then.