The story may have some glimmer of reality, but it is not completely true.
When Hans-Adam married Countess Marie-Aglaë in 1967, the generous uncle (Prince Ulrich, husband of Princess Mathilde [née Fürstin von dem Bussche-Haddenhausen]) was dead for a while (1938) then it is likely that the generous were the Dowager Princess herself or her son Prince Franz Ulrich.