There are no “belief system of some scientists” involved in obtaining dates. As a former paleobiologist, I know this. Dates in geological time can be relative or absolute.

They are relative on the basis of centuries worth of data in biostratigrapy, correlating geological formations from one region to another on the basis of key characteristic fossils which are known as index fossils (Contrary to creationist claims to the contrary, this is not a tautology since biostratigraphers have recognized certain species that are geographically widespread for them to be used successfully in assigning relative ages of, for example, Cretaceous marine rocks in Texas with those in Delaware and New Jersey. They can assign ages to other fossils found in these rocks based on the occurrence of the index fossils associated with these marine sedimentary rocks – what would be termed more accurately as sedimentary rock sequences or strata – in these locations.).

Absolute ages are based on radiometric dating (which depends on the decay rate of radioactive elements, and these are absolute in the sense that they are accurate at a 95% or better probability.). In the case of the Liaoning fauna, the dates were derived by dating igneous rocks above and below the strata (sedimentary rock sequences) containing these mammalian fossils. That is why these Chinese researchers – whom I might add have been collaborating with colleagues at New York City’s American Museum of Natural History and elsewhere for years – can be reasonably confident about the approximate age of these fossils.

You can find more information about the Liaoning fauna here:

http://www.amnh.org/exhibitions/dinosaurs/