Context. A new hypothesis is offered to explain the so-called ribbon feature appearing in the all-sky flux maps of energetic neutral atoms presently observed with the IBEX spacecraft, namely that the ribbon is a consequence of inhomogeneities in the local interstellar medium. Aims. The study aims at a detailed presentation of this hypothesis and its implications for the interpretation of ENA measurements with IBEX. Methods. Theoretical considerations regarding three different topics, namely IBEX measurements related to high-energy neutral atoms, Lyman-α observations (made with the Voyager 1 spacecraft) related to low-energy neutral atoms, and astronomical data related to the structure of the interstellar medium, are critically discussed in order to corroborate the hypothesis. Results. It is found that inhomogeneities in the local interstellar medium can explain not only the IBEX ribbon and outer heliospheric Lyman-α observations, but can also account for the interstellar Lyman-α absorption that could only with difficulty be fully attributed to the hydrogen wall in the outer heliosheath if the heliospheric bow shock would indeed be absent. Conclusions. The IBEX observations of the ribbon provide a unique opportunity to learn more about the nature of the interstellar medium surrounding the heliosphere.