She denied Indy an absolutely unique opportunity to end his life on his own terms
What's more is that her reasoning, the fear that he'd change history, ignores that it has previously been established in the scene where they find Archimedes' tomb that everything which will happen in the past has already happened. If not, the watch wouldn't be there and there wouldn't be any 'modern' technology on the engraving. By implication, anything Indy does during his trip to Syracuse has already been accounted for by history, so it does not matter whether he stays or is taken back. A better reason would have been that given Indy's advancing age, he might want to reconsider his plans to stay in Syracuse purely for the lack of modern plumbing.