Deep Neural Networks (DNNs) are becoming a crucial component of modern software systems, but they are prone to fail under conditions that are different from the ones observed during training (out-of-distribution inputs) or on inputs that are truly ambiguous, i.e., inputs that admit multiple classes with nonzero probability in their labels. Recent work proposed DNN supervisors to detect high-uncertainty inputs before their possible misclassification leads to any harm. To test and compare the capabilities of DNN supervisors, researchers proposed test generation techniques, to focus the testing effort on high-uncertainty inputs that should be recognized as anomalous by supervisors. However, existing test generators aim to produce out-of-distribution inputs. No existing model- and supervisor independent technique targets the generation of truly ambiguous test inputs, i.e., inputs that admit multiple classes according to expert human judgment. In this paper, we propose a novel way to generate ambiguous inputs to test DNN supervisors and used it to empirically compare several existing supervisor techniques. In particular, we propose AmbiGuess to generate ambiguous samples for image classification problems. AmbiGuess is based on gradient-guided sampling in the latent space of a regularized adversarial autoencoder. Moreover, we conducted what is -- to the best of our knowledge -- the most extensive comparative study of DNN supervisors, considering their capabilities to detect 4 distinct types of high-uncertainty inputs, including truly ambiguous ones. We find that the tested supervisors' capabilities are complementary: Those best suited to detect true ambiguity perform worse on invalid, out-of-distribution and adversarial inputs and vice-versa.