It seems like the default solver setting is single numeric precision. Is this true? I was surprised to find that changing this setting in the Analysis configuration (bulk data section) changes not only the output format, but also the results (so, the stiffness matrix too). I have a simple model which I would expect would be sensitive to numerical precision, but I did not expect this setting to affect anything except the results output format. It seems like a very risky default to me. The AUTOSPC default is also pretty questionable, but that's another topic.
This setting only controls the precision of the bulk data input. It does not change any setting internal to Nastran calculations, they are always full double precision(element routines,solver etc). If you see answer changes by using this setting, it is because your model either has very small or very large dimensions where 8 digits on the bulk data input is not sufficient. To understand the limitations of the default 8 column input, see the QRG on input syntax and I think it will be obvious there are models where the default is not accurate enough.