Are there adversarial inputs for randomized quicksort?
There are implementations of Quicksort (the partitioning algorithm, specifically) which deal badly with duplicates. No matter how much you randomize -- shuffling the input, random choice of the pivot, random choice of the pivot with sampling, ... -- if all entries are the same (or there are only constantly many distinct values), these bad implementations will result in worst-case behaviour, always.

You can find details e.g. here and in the literature.

Note bene: The reason why many TCSists would claim the opposite with a passion it that they forget that most classical analyses are performed under permutation models. That does not give the whole truth, though, particularly if you use sorting in practice. Duplicates are relevant, for instance if you sort lists of binary values.