What's the field strength of the instrument the spec was acquired on? If it was an old 90 MHz instrument, then the reason you don't see splitting is because its a crappy instrument that lacks the power to resolve fine structures.
Nonaromatic cycles tend to give pretty bad looking 1H spectra because their protons are conformationally restricted, which places them in distinct electronic environments. In a cyclohexane, for instance, the axial and equatorial protons have different environments and will yield different chemical shift values. Furthermore, the axial and equatorial protons which share a carbon can couple and will exhibit splitting, as well as distinct splitting from the neighboring axial and equatorial protons. Combine this with ring flips, and you've a recipe for a really bad looking spectrum. An instrument with a weak magnet won't be able to resolve this splitting and they will just look like broad singlets.