Twilight isn't your typical Canterlot noble snob either, maybe her parents weren't that wealthy, more like poor, so being semi adopted by the ruler of all ponies is a jackpot and they let her have her perfect life with the princess.
Her fear of disappointing Celestia is like that of a child towards its parents.
All this will be shattered with the season finale episode of course, Twilights parents will surely be there.