The rubber hand illusion is a perceptual illusion of perceiving an object like a model hand as part of the own body. The question whether the illusion can be induced with noncorporal objects that do not look like a human body part is not perfectly resolved yet. In this study, we directly assessed the subjective experience of two different components within the illusion (i.e., ownership and referral of touch) when a model hand and a balloon are stimulated. We observed significantly stronger illusion ratings for the hand as compared with the balloon, and only the hand ratings showed a clear affirmation of the illusion. We further conclude that (a) a significant difference between synchronous and asynchronous conditions may not be sufficient to argue for the successful induction of the illusion and (b) the subcomponents show a different pattern in the different conditions, which may lead to alternative interpretations. These observations call for a more fine-grained interpretation of questionnaire data in rubber hand illusion studies.