The only weakness I can find in the "despotic tyrant" expression is that indeed there is some tautology and you do not necessarily need both words. Both are Greek words; in modern greek the latter (tyrant) is a stronger word than the former (despot) and I can not think of a context where you would see both of them together. In ancient Greek the same applies although you could see both of them in the same sentence as a way of describing a deterioration in political governance for example from enlightened despotism to tyranny.
Since this is a test in History and not in language etymology all of the above is beside the point and the students are completely without an excuse. There is a Greek word to describe their conditition: "lexipenia" which means being literally poor in words.
Ok, more after a big discussion with DH who is a big fan of 20th century history. Tyranny in ancient Greek did not necessarily had the implications of something bad or good as there were both good and bad tyrants in the Greek hisotry; hence the despotic characterisation is not redundant. However tyranny implies coming to power by unconventional methods and in this respect Hitler was not a tyrant as he was democratically electeted (in fact at that time no party obtained a majority following the elections, and so different parties were invited by the president to attempt to form a government and Hitler's party succeeded in doing so.)
I sincerely hope that the students' objections are stemming from purely etymological objections that may affect the "yes" or "no" tone of their answer rather than not knowing these words at all