I can't agree that its a lofty statement; Mary was a terrible snob. Her parents had planned to marry her into the royal family of Spain, but hastily married her to the son of the Stadholder instead, in the belief that the Stadholder would send the Dutch army to help Charles if war broke out. The Stadholder could not help Charles with troops, and this was only realized after Henrietta visited Holland in 1642. Mary, who grew up expecting to become a Queen, and who believed that the Stadholder could and should help her father, took out her anger and disappointment on her new family.
The Stadholder had been fighting a war with Spain for Dutch independence for many years, and was a real hero, yet Mary kept him standing and hatless in her presence, though he was ill. Mary also asserted herself over her mother-in-law and sisters-in-law, and was regularly rude to them, with Henrietta's full approval.
There is no express evidence, besides Liselotte's tale, for the fact that Sophia and her sisters disliked Mary and vice-versa. However, its telling that Sophia did not call on Mary, and said what she did to Liselotte about revenging them on her. Liselotte had an excellent memory, and I can't imagine why she would have made this up.