Delphine certainly had the right to pursue her paternity cause, but it was how she went about it. She portrayed herself growing up as practically penniless, living in a shed, so to speak. She missed out on being a Royal. In reality, her legal father Jacques Boel loved her and she had a privileged life as he was one of the wealthiest men in Belgium and possibly Europe. Delphine lacked for nothing, he legal father was far wealthier than the Belgian Royal Family.
Delphine's parents divorced and it's believed that her mother Jacqueline started pushing Delphine towards the paternity issue and continued throughout. Delphine herself didn't need a whole lot of pushing especially when her legal father disowned her and cut her out of his will. The public ate up her story and sympathized with Delphine.
Her treatment of Albert and Paola through the entire process was deplorable. Paola wasn't a party in the situation and didn't deserve the slurs and horrible things Delphine put out. She put on a real con job with the public in regards to her life without "her father, the King."
Laurent was her big supporter and that didn't help matters at all, either.