Aims: We investigate Galactic bulge planetary nebulae without emission-line central stars for which peculiar infrared spectra have been obtained with the Spitzer Space Telescope, including the simultaneous signs of oxygen and carbon based dust. Three separate sub-groups can be defined characterized by the different chemical composition of the dust and the presence of crystalline and amorphous silicates. Methods: We use literature data to analyze the different nebular properties and deduce both the evolutionary status and the origin of these three groups. In particular, we check whether there are signs of evolutionary links between dual-dust chemistry planetary nebulae without detected emission-line central stars and those with emission-line stars. Results: Our primary finding is that the classification based on the dust properties is reflected in the more general properties of these planetary nebulae. However, some observed properties are difficult to relate to the common view of planetary nebulae. In particular, it is challenging to interpret the peculiar gas chemical composition of many analyzed objects in the standard picture of the evolution of planetary nebulae progenitors. We confirm that the dual-dust chemistry phenomenon is not limited to planetary nebulae with emission-line central stars. Conclusions: Our results clearly indicate that there is no unique road to the formation of planetary nebulae even in a homogeneous environment such as the Galactic bulge. The evolution of a single asymptotic giant branch star may lead to the formation of different types of planetary nebulae. In addition, the evolution in a close binary system should sometimes also be considered. Based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407.